Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras

Gorenstein-projective module is an important research topic in relative homological algebra, representation theory of algebras, triangulated categories, and algebraic geometry (especially in singularity theory). For a given algebra A, how to construct all the Gorenstein-projective A-modules is a fun...

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Autor principal: Dadi Asefa
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Publicado: Hindawi Limited 2021
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Acceso en línea:https://doaj.org/article/504a2950c6f540c1a11a5a5940b32943
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spelling oai:doaj.org-article:504a2950c6f540c1a11a5a5940b329432021-11-29T00:56:38ZGorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras2314-478510.1155/2021/8127282https://doaj.org/article/504a2950c6f540c1a11a5a5940b329432021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/8127282https://doaj.org/toc/2314-4785Gorenstein-projective module is an important research topic in relative homological algebra, representation theory of algebras, triangulated categories, and algebraic geometry (especially in singularity theory). For a given algebra A, how to construct all the Gorenstein-projective A-modules is a fundamental problem in Gorenstein homological algebra. In this paper, we describe all complete projective resolutions over an upper triangular Artin algebra Λ=AMBA0B. We also give a necessary and sufficient condition for all finitely generated Gorenstein-projective modules over Λ=AMBA0B.Dadi AsefaHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution DOAJ
collection DOAJ
language EN
topic Mathematics
QA1-939
spellingShingle Mathematics
QA1-939
Dadi Asefa
Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras
description Gorenstein-projective module is an important research topic in relative homological algebra, representation theory of algebras, triangulated categories, and algebraic geometry (especially in singularity theory). For a given algebra A, how to construct all the Gorenstein-projective A-modules is a fundamental problem in Gorenstein homological algebra. In this paper, we describe all complete projective resolutions over an upper triangular Artin algebra Λ=AMBA0B. We also give a necessary and sufficient condition for all finitely generated Gorenstein-projective modules over Λ=AMBA0B.
format article
author Dadi Asefa
author_facet Dadi Asefa
author_sort Dadi Asefa
title Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras
title_short Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras
title_full Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras
title_fullStr Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras
title_full_unstemmed Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras
title_sort gorenstein-projective modules over upper triangular matrix artin algebras
publisher Hindawi Limited
publishDate 2021
url https://doaj.org/article/504a2950c6f540c1a11a5a5940b32943
work_keys_str_mv AT dadiasefa gorensteinprojectivemodulesoveruppertriangularmatrixartinalgebras
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