On Artin algebras arising from Morita contexts release_6utteynvzfdo7ef3o6xieluvdy

Abstract

We study Morita rings Λ_(ϕ,ψ)=(smallmatrix A &_AN_B_BM_A & B smallmatrix) in the context of Artin algebras from various perspectives. First we study covariant finite, contravariant finite, and functorially finite subcategories of the module category of a Morita ring when the bimodule homomorphisms ϕ and ψ are zero. Further we give bounds for the global dimension of a Morita ring Λ_(0,0), regarded as an Artin algebra, in terms of the global dimensions of A and B in the case when both ϕ and ψ are zero. We illustrate our bounds with some examples. Finally we investigate when a Morita ring is a Gorenstein Artin algebra and then we determine all the Gorenstein-projective modules over the Morita ring with A=N=M=B=Λ, where Λ is an Artin algebra.
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