On Artin Algebras Arising from Morita Contexts

We study Morita rings (Lambda _{(phi ,psi )}=left (begin {array}{cc}A &_{A}N_{B} _{B}M_{A} & B end {array}right )) in the context of Artin algebras from various perspectives. First we study covariantly finite, contravariantly finite, and functorially finite subcategories of the module category of a Morita ring when the bimodule homomorphisms (phi ) and (psi ) are zero. Further we give bounds for the global dimension of a Morita ring (Lambda _{(0,0)}) , as an Artin algebra, in terms of the global dimensions of A and B in the case when both (phi ) and (psi ) 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 (Lambda _{phi ,psi }) in case (A=N=M=B) and A an Artin algebra.