The Weil descent functor in the category of algebras with free operators

We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R →...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Mohamed, Shezad [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Weil descent Left adjoints Differential algebra Difference algebra Fields with operators

Übergeordnetes Werk:	Enthalten in: Journal of algebra - San Diego, Calif. : Elsevier, 1964, 640, Seite 216-252
Übergeordnetes Werk:	volume:640 ; pages:216-252

DOI / URN:	10.1016/j.jalgebra.2023.10.029

Katalog-ID:	ELV066037131

Internformat


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520			\|a We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere.
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650		4	\|a Differential algebra
650		4	\|a Difference algebra
650		4	\|a Fields with operators
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allfields	10.1016/j.jalgebra.2023.10.029 doi (DE-627)ELV066037131 (ELSEVIER)S0021-8693(23)00554-9 DE-627 ger DE-627 rda eng 510 VZ 31.20 bkl Mohamed, Shezad verfasserin (orcid)0000-0003-3498-6878 aut The Weil descent functor in the category of algebras with free operators 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere. Weil descent Left adjoints Differential algebra Difference algebra Fields with operators Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 640, Seite 216-252 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:640 pages:216-252 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines VZ AR 640 216-252
spelling	10.1016/j.jalgebra.2023.10.029 doi (DE-627)ELV066037131 (ELSEVIER)S0021-8693(23)00554-9 DE-627 ger DE-627 rda eng 510 VZ 31.20 bkl Mohamed, Shezad verfasserin (orcid)0000-0003-3498-6878 aut The Weil descent functor in the category of algebras with free operators 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere. Weil descent Left adjoints Differential algebra Difference algebra Fields with operators Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 640, Seite 216-252 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:640 pages:216-252 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines VZ AR 640 216-252
allfields_unstemmed	10.1016/j.jalgebra.2023.10.029 doi (DE-627)ELV066037131 (ELSEVIER)S0021-8693(23)00554-9 DE-627 ger DE-627 rda eng 510 VZ 31.20 bkl Mohamed, Shezad verfasserin (orcid)0000-0003-3498-6878 aut The Weil descent functor in the category of algebras with free operators 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere. Weil descent Left adjoints Differential algebra Difference algebra Fields with operators Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 640, Seite 216-252 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:640 pages:216-252 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines VZ AR 640 216-252
allfieldsGer	10.1016/j.jalgebra.2023.10.029 doi (DE-627)ELV066037131 (ELSEVIER)S0021-8693(23)00554-9 DE-627 ger DE-627 rda eng 510 VZ 31.20 bkl Mohamed, Shezad verfasserin (orcid)0000-0003-3498-6878 aut The Weil descent functor in the category of algebras with free operators 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere. Weil descent Left adjoints Differential algebra Difference algebra Fields with operators Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 640, Seite 216-252 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:640 pages:216-252 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines VZ AR 640 216-252
allfieldsSound	10.1016/j.jalgebra.2023.10.029 doi (DE-627)ELV066037131 (ELSEVIER)S0021-8693(23)00554-9 DE-627 ger DE-627 rda eng 510 VZ 31.20 bkl Mohamed, Shezad verfasserin (orcid)0000-0003-3498-6878 aut The Weil descent functor in the category of algebras with free operators 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere. Weil descent Left adjoints Differential algebra Difference algebra Fields with operators Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 640, Seite 216-252 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:640 pages:216-252 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 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_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 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_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines VZ AR 640 216-252
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The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. 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author	Mohamed, Shezad
spellingShingle	Mohamed, Shezad ddc 510 bkl 31.20 misc Weil descent misc Left adjoints misc Differential algebra misc Difference algebra misc Fields with operators The Weil descent functor in the category of algebras with free operators
authorStr	Mohamed, Shezad
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topic_title	510 VZ 31.20 bkl The Weil descent functor in the category of algebras with free operators Weil descent Left adjoints Differential algebra Difference algebra Fields with operators
topic	ddc 510 bkl 31.20 misc Weil descent misc Left adjoints misc Differential algebra misc Difference algebra misc Fields with operators
topic_unstemmed	ddc 510 bkl 31.20 misc Weil descent misc Left adjoints misc Differential algebra misc Difference algebra misc Fields with operators
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title	The Weil descent functor in the category of algebras with free operators
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title_full	The Weil descent functor in the category of algebras with free operators
author_sort	Mohamed, Shezad
journal	Journal of algebra
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title_sort	the weil descent functor in the category of algebras with free operators
title_auth	The Weil descent functor in the category of algebras with free operators
abstract	We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere.
abstractGer	We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere.
abstract_unstemmed	We prove that there exists a version of Weil descent, or Weil restriction, in the category of D -algebras. The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. In particular, this yields the existence of the Weil descent functor in the category of difference algebras, which, to our knowledge, does not appear elsewhere.
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title_short	The Weil descent functor in the category of algebras with free operators
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doi_str	10.1016/j.jalgebra.2023.10.029
up_date	2024-07-07T01:06:55.614Z
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The objects of this category are k-algebras R equipped with a homomorphism e : R → R ⊗ k D for some fixed field k and finite-dimensional k-algebra D . We do this under a mild assumption on the so-called associated endomorphisms. 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The Weil descent functor in the category of algebras with free operators

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