1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring

Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing s...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Groenewald, Nico [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	1-absorbing prime submodule Weakly 1-absorbing prime submodule

Anmerkung:	© The Author(s) 2023

Übergeordnetes Werk:	Enthalten in: Afrika Matematika - Berlin : Springer, 2011, 34(2023), 3 vom: 22. Juli
Übergeordnetes Werk:	volume:34 ; year:2023 ; number:3 ; day:22 ; month:07

Links:	Volltext

DOI / URN:	10.1007/s13370-023-01094-0

Katalog-ID:	SPR052348873

Internformat


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520			\|a Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. Various properties and characterizations of these classes of submodules are considered.
650		4	\|a 1-absorbing prime submodule \|7 (dpeaa)DE-He213
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773	0	8	\|i Enthalten in \|t Afrika Matematika \|d Berlin : Springer, 2011 \|g 34(2023), 3 vom: 22. Juli \|w (DE-627)646517430 \|w (DE-600)2594298-0 \|x 2190-7668 \|7 nnns
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912			\|a GBV_USEFLAG_A
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912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
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912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
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951			\|a AR
952			\|d 34 \|j 2023 \|e 3 \|b 22 \|c 07

Indexfelder

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allfields	10.1007/s13370-023-01094-0 doi (DE-627)SPR052348873 (SPR)s13370-023-01094-0-e DE-627 ger DE-627 rakwb eng Groenewald, Nico verfasserin (orcid)0000-0003-2843-3046 aut 1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. Various properties and characterizations of these classes of submodules are considered. 1-absorbing prime submodule (dpeaa)DE-He213 Weakly 1-absorbing prime submodule (dpeaa)DE-He213 Enthalten in Afrika Matematika Berlin : Springer, 2011 34(2023), 3 vom: 22. Juli (DE-627)646517430 (DE-600)2594298-0 2190-7668 nnns volume:34 year:2023 number:3 day:22 month:07 https://dx.doi.org/10.1007/s13370-023-01094-0 kostenfrei 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 34 2023 3 22 07
spelling	10.1007/s13370-023-01094-0 doi (DE-627)SPR052348873 (SPR)s13370-023-01094-0-e DE-627 ger DE-627 rakwb eng Groenewald, Nico verfasserin (orcid)0000-0003-2843-3046 aut 1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. Various properties and characterizations of these classes of submodules are considered. 1-absorbing prime submodule (dpeaa)DE-He213 Weakly 1-absorbing prime submodule (dpeaa)DE-He213 Enthalten in Afrika Matematika Berlin : Springer, 2011 34(2023), 3 vom: 22. Juli (DE-627)646517430 (DE-600)2594298-0 2190-7668 nnns volume:34 year:2023 number:3 day:22 month:07 https://dx.doi.org/10.1007/s13370-023-01094-0 kostenfrei 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 34 2023 3 22 07
allfields_unstemmed	10.1007/s13370-023-01094-0 doi (DE-627)SPR052348873 (SPR)s13370-023-01094-0-e DE-627 ger DE-627 rakwb eng Groenewald, Nico verfasserin (orcid)0000-0003-2843-3046 aut 1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. Various properties and characterizations of these classes of submodules are considered. 1-absorbing prime submodule (dpeaa)DE-He213 Weakly 1-absorbing prime submodule (dpeaa)DE-He213 Enthalten in Afrika Matematika Berlin : Springer, 2011 34(2023), 3 vom: 22. Juli (DE-627)646517430 (DE-600)2594298-0 2190-7668 nnns volume:34 year:2023 number:3 day:22 month:07 https://dx.doi.org/10.1007/s13370-023-01094-0 kostenfrei 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 34 2023 3 22 07
allfieldsGer	10.1007/s13370-023-01094-0 doi (DE-627)SPR052348873 (SPR)s13370-023-01094-0-e DE-627 ger DE-627 rakwb eng Groenewald, Nico verfasserin (orcid)0000-0003-2843-3046 aut 1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. Various properties and characterizations of these classes of submodules are considered. 1-absorbing prime submodule (dpeaa)DE-He213 Weakly 1-absorbing prime submodule (dpeaa)DE-He213 Enthalten in Afrika Matematika Berlin : Springer, 2011 34(2023), 3 vom: 22. Juli (DE-627)646517430 (DE-600)2594298-0 2190-7668 nnns volume:34 year:2023 number:3 day:22 month:07 https://dx.doi.org/10.1007/s13370-023-01094-0 kostenfrei 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 34 2023 3 22 07
allfieldsSound	10.1007/s13370-023-01094-0 doi (DE-627)SPR052348873 (SPR)s13370-023-01094-0-e DE-627 ger DE-627 rakwb eng Groenewald, Nico verfasserin (orcid)0000-0003-2843-3046 aut 1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. Various properties and characterizations of these classes of submodules are considered. 1-absorbing prime submodule (dpeaa)DE-He213 Weakly 1-absorbing prime submodule (dpeaa)DE-He213 Enthalten in Afrika Matematika Berlin : Springer, 2011 34(2023), 3 vom: 22. Juli (DE-627)646517430 (DE-600)2594298-0 2190-7668 nnns volume:34 year:2023 number:3 day:22 month:07 https://dx.doi.org/10.1007/s13370-023-01094-0 kostenfrei 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 34 2023 3 22 07
language	English
source	Enthalten in Afrika Matematika 34(2023), 3 vom: 22. Juli volume:34 year:2023 number:3 day:22 month:07
sourceStr	Enthalten in Afrika Matematika 34(2023), 3 vom: 22. Juli volume:34 year:2023 number:3 day:22 month:07
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	1-absorbing prime submodule Weakly 1-absorbing prime submodule
isfreeaccess_bool	true
container_title	Afrika Matematika
authorswithroles_txt_mv	Groenewald, Nico @@aut@@
publishDateDaySort_date	2023-07-22T00:00:00Z
hierarchy_top_id	646517430
id	SPR052348873
language_de	englisch
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author	Groenewald, Nico
spellingShingle	Groenewald, Nico misc 1-absorbing prime submodule misc Weakly 1-absorbing prime submodule 1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring
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topic_title	1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring 1-absorbing prime submodule (dpeaa)DE-He213 Weakly 1-absorbing prime submodule (dpeaa)DE-He213
topic	misc 1-absorbing prime submodule misc Weakly 1-absorbing prime submodule
topic_unstemmed	misc 1-absorbing prime submodule misc Weakly 1-absorbing prime submodule
topic_browse	misc 1-absorbing prime submodule misc Weakly 1-absorbing prime submodule
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring
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title_full	1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring
author_sort	Groenewald, Nico
journal	Afrika Matematika
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author_browse	Groenewald, Nico
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author-letter	Groenewald, Nico
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title_sort	1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring
title_auth	1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring
abstract	Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. Various properties and characterizations of these classes of submodules are considered. © The Author(s) 2023
abstractGer	Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. Various properties and characterizations of these classes of submodules are considered. © The Author(s) 2023
abstract_unstemmed	Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. Various properties and characterizations of these classes of submodules are considered. © The Author(s) 2023
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title_short	1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring
url	https://dx.doi.org/10.1007/s13370-023-01094-0
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up_date	2024-07-04T02:27:48.488Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR052348873</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230818064734.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230723s2023 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s13370-023-01094-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR052348873</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s13370-023-01094-0-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Groenewald, Nico</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-2843-3046</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2023</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly 1-absorbing prime submodules of a unital module over a noncommutative ring with nonzero identity. This is a new class of submodules between prime submodules (weakly prime submodules) and 2-absorbing submodules (weakly 2-absorbing submodules). Let R be a noncommutative ring with a nonzero identity %$1\ne 0%$ and M an R-module. A proper submdule P of M is said to be a 1-absorbing prime submodule (weakly 1-absorbing prime submodule) if for all nonunits %$x,y\in R%$ and %$m\in M%$ with xRyRm%$\subseteq %$P%$(\left\{ 0\right\} \ne %$xRyRm%$\subseteq P)%$, then %$xy\in (M:_{R}P)%$ or %$m\in P%$. 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1-absorbing and weakly 1-absorbing prime submodules of a module over a noncommutative ring

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