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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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) |
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Mathematics QA1-939 |
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Mathematics QA1-939 Dadi Asefa Gorenstein-Projective Modules over Upper Triangular Matrix Artin Algebras |
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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. |
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author |
Dadi Asefa |
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Dadi Asefa |
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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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1718407705766395904 |