On Artin algebras arising from Morita contexts release_6utteynvzfdo7ef3o6xieluvdy

by Edward L. Green, Chrysostomos Psaroudakis

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abstracts[] {'sha1': '8511b60c4e3a39f7681f46d280f0da6582fcbec5', 'content': 'We study Morita rings Λ_(ϕ,ψ)=(smallmatrix A\n&_AN_B_BM_A & B smallmatrix) in the context of Artin algebras from\nvarious perspectives. First we study covariant finite, contravariant finite,\nand functorially finite subcategories of the module category of a Morita ring\nwhen the bimodule homomorphisms ϕ and ψ are zero. Further we give\nbounds for the global dimension of a Morita ring Λ_(0,0), regarded as\nan Artin algebra, in terms of the global dimensions of A and B in the case\nwhen both ϕ and ψ are zero. We illustrate our bounds with some\nexamples. Finally we investigate when a Morita ring is a Gorenstein Artin\nalgebra and then we determine all the Gorenstein-projective modules over the\nMorita ring with A=N=M=B=Λ, where Λ is an Artin algebra.', 'mimetype': 'text/plain', 'lang': 'en'}
{'sha1': '9c9eef88bbd33213bca6d5af0672b087881985b7', 'content': 'We study Morita rings $\\Lambda_{(\\phi,\\psi)}=\\bigl({smallmatrix} A\n&_AN_B_BM_A & B {smallmatrix}\\bigr)$ in the context of Artin algebras from\nvarious perspectives. First we study covariant finite, contravariant finite,\nand functorially finite subcategories of the module category of a Morita ring\nwhen the bimodule homomorphisms $\\phi$ and $\\psi$ are zero. Further we give\nbounds for the global dimension of a Morita ring $\\Lambda_{(0,0)}$, regarded as\nan Artin algebra, in terms of the global dimensions of $A$ and $B$ in the case\nwhen both $\\phi$ and $\\psi$ are zero. We illustrate our bounds with some\nexamples. Finally we investigate when a Morita ring is a Gorenstein Artin\nalgebra and then we determine all the Gorenstein-projective modules over the\nMorita ring with $A=N=M=B=\\Lambda$, where $\\Lambda$ is an Artin algebra.', 'mimetype': 'application/x-latex', 'lang': 'en'}
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{'index': 1, 'creator_id': None, 'creator': None, 'raw_name': 'Chrysostomos Psaroudakis', 'given_name': None, 'surname': None, 'role': 'author', 'raw_affiliation': None, 'extra': None}
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license_slug ARXIV-1.0
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release_date 2013-03-08
release_stage submitted
release_type article
release_year 2013
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title On Artin algebras arising from Morita contexts
version v1
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arxiv.base_id 1303.2083
arxiv.categories ['math.RT', 'math.CT', 'math.RA']
arxiv.comments 29 pages, revised version
superceded True