{"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"}],"refs":[],"contribs":[{"index":0,"raw_name":"Edward L. Green","role":"author"},{"index":1,"raw_name":"Chrysostomos Psaroudakis","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v1","ext_ids":{"arxiv":"1303.2083v1"},"release_year":2013,"release_date":"2013-03-08","release_stage":"submitted","release_type":"article","work_id":"awxvh2mhenhwpbsobtvder7rdq","title":"On Artin algebras arising from Morita contexts","state":"active","ident":"6utteynvzfdo7ef3o6xieluvdy","revision":"0875a247-96ee-4710-96f6-23b3f15875c2","extra":{"arxiv":{"base_id":"1303.2083","categories":["math.RT","math.CT","math.RA"],"comments":"29 pages, revised version"},"superceded":true}}