The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension
Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Dabbabi, Abdelamir [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Rendiconti del Circolo Matematico di Palermo - Milano : Springer Italia, 1884, 73(2023), 2 vom: 22. Sept., Seite 757-771 |
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| Übergeordnetes Werk: |
volume:73 ; year:2023 ; number:2 ; day:22 ; month:09 ; pages:757-771 |
| Links: |
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| DOI / URN: |
10.1007/s12215-023-00951-y |
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| Katalog-ID: |
SPR05490742X |
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| 520 | |a Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. Note that the main purpose of this paper is studying the algebraic side of this ring construction. | ||
| 650 | 4 | |a -Noetherian rings |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Infinite product |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Krull dimension |7 (dpeaa)DE-He213 | |
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10.1007/s12215-023-00951-y doi (DE-627)SPR05490742X (SPR)s12215-023-00951-y-e DE-627 ger DE-627 rakwb eng Dabbabi, Abdelamir verfasserin aut The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. Note that the main purpose of this paper is studying the algebraic side of this ring construction. -Noetherian rings (dpeaa)DE-He213 Infinite product (dpeaa)DE-He213 Krull dimension (dpeaa)DE-He213 Benhissi, Ali aut Enthalten in Rendiconti del Circolo Matematico di Palermo Milano : Springer Italia, 1884 73(2023), 2 vom: 22. Sept., Seite 757-771 (DE-627)560173067 (DE-600)2415092-7 0009-725X nnns volume:73 year:2023 number:2 day:22 month:09 pages:757-771 https://dx.doi.org/10.1007/s12215-023-00951-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2023 2 22 09 757-771 |
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10.1007/s12215-023-00951-y doi (DE-627)SPR05490742X (SPR)s12215-023-00951-y-e DE-627 ger DE-627 rakwb eng Dabbabi, Abdelamir verfasserin aut The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. Note that the main purpose of this paper is studying the algebraic side of this ring construction. -Noetherian rings (dpeaa)DE-He213 Infinite product (dpeaa)DE-He213 Krull dimension (dpeaa)DE-He213 Benhissi, Ali aut Enthalten in Rendiconti del Circolo Matematico di Palermo Milano : Springer Italia, 1884 73(2023), 2 vom: 22. Sept., Seite 757-771 (DE-627)560173067 (DE-600)2415092-7 0009-725X nnns volume:73 year:2023 number:2 day:22 month:09 pages:757-771 https://dx.doi.org/10.1007/s12215-023-00951-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2023 2 22 09 757-771 |
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10.1007/s12215-023-00951-y doi (DE-627)SPR05490742X (SPR)s12215-023-00951-y-e DE-627 ger DE-627 rakwb eng Dabbabi, Abdelamir verfasserin aut The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. Note that the main purpose of this paper is studying the algebraic side of this ring construction. -Noetherian rings (dpeaa)DE-He213 Infinite product (dpeaa)DE-He213 Krull dimension (dpeaa)DE-He213 Benhissi, Ali aut Enthalten in Rendiconti del Circolo Matematico di Palermo Milano : Springer Italia, 1884 73(2023), 2 vom: 22. Sept., Seite 757-771 (DE-627)560173067 (DE-600)2415092-7 0009-725X nnns volume:73 year:2023 number:2 day:22 month:09 pages:757-771 https://dx.doi.org/10.1007/s12215-023-00951-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2023 2 22 09 757-771 |
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10.1007/s12215-023-00951-y doi (DE-627)SPR05490742X (SPR)s12215-023-00951-y-e DE-627 ger DE-627 rakwb eng Dabbabi, Abdelamir verfasserin aut The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. Note that the main purpose of this paper is studying the algebraic side of this ring construction. -Noetherian rings (dpeaa)DE-He213 Infinite product (dpeaa)DE-He213 Krull dimension (dpeaa)DE-He213 Benhissi, Ali aut Enthalten in Rendiconti del Circolo Matematico di Palermo Milano : Springer Italia, 1884 73(2023), 2 vom: 22. Sept., Seite 757-771 (DE-627)560173067 (DE-600)2415092-7 0009-725X nnns volume:73 year:2023 number:2 day:22 month:09 pages:757-771 https://dx.doi.org/10.1007/s12215-023-00951-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2023 2 22 09 757-771 |
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10.1007/s12215-023-00951-y doi (DE-627)SPR05490742X (SPR)s12215-023-00951-y-e DE-627 ger DE-627 rakwb eng Dabbabi, Abdelamir verfasserin aut The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. Note that the main purpose of this paper is studying the algebraic side of this ring construction. -Noetherian rings (dpeaa)DE-He213 Infinite product (dpeaa)DE-He213 Krull dimension (dpeaa)DE-He213 Benhissi, Ali aut Enthalten in Rendiconti del Circolo Matematico di Palermo Milano : Springer Italia, 1884 73(2023), 2 vom: 22. Sept., Seite 757-771 (DE-627)560173067 (DE-600)2415092-7 0009-725X nnns volume:73 year:2023 number:2 day:22 month:09 pages:757-771 https://dx.doi.org/10.1007/s12215-023-00951-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 73 2023 2 22 09 757-771 |
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. 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Dabbabi, Abdelamir |
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Dabbabi, Abdelamir misc -Noetherian rings misc Infinite product misc Krull dimension The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension |
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The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension -Noetherian rings (dpeaa)DE-He213 Infinite product (dpeaa)DE-He213 Krull dimension (dpeaa)DE-He213 |
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s-noetherian ring %$a[x,y;\lambda ]%$ and krull dimension |
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The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension |
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Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. Note that the main purpose of this paper is studying the algebraic side of this ring construction. © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. Note that the main purpose of this paper is studying the algebraic side of this ring construction. © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract Let A be a ring, %$S\subseteq A%$ a multiplicative set and %$\lambda :{\mathbb {R}}_{\ge 0}\longrightarrow {\mathbb {R}}_{\ge 0}%$ a nonzero increasing function. In this paper, we study the S-Noetherianity and the Krull dimension of subrings %$A[X,Y;\lambda ]%$ of %$A[X][[Y]]=A[X_1,\cdots ,X_n][[Y_1,\cdots ,Y_m]]%$. Such rings are obtained from elements of A[X][[Y]] by bounding their total X-degree above by %$\lambda %$ on their Y-degree. However, we give a necessary and sufficient condition for the ring %$A[X,Y;\lambda ]%$ to be S-Noetherian when %$\lambda %$ grows at least as fast as linear. It tuns out that the ring %$A[X,Y;\lambda ]%$ is S-Noetherian for a large class of functions %$\lambda %$ including functions of the form %$\lambda (x)=e^{rx^t}%$ where %$r>0%$ and %$t\le 1%$. This result allows us to give a new class of Noetherian rings and modules. In the second part of this paper, we define the infinite product in the ring %$A[X,Y;\lambda ]%$ to give a sufficient condition so that the Krull dimension of the ring %$A[X,Y;\lambda ]%$ is infinite. Note that the main purpose of this paper is studying the algebraic side of this ring construction. © The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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The S-Noetherian ring %$A[X,Y;\lambda ]%$ and Krull dimension |
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https://dx.doi.org/10.1007/s12215-023-00951-y |
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Benhissi, Ali |
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10.1007/s12215-023-00951-y |
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2024-07-04T03:28:04.932Z |
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| score |
7.39935 |