Injective modules over pseudo-krullian orders

Abstract

We introduce a new class of rings, pseudo-krullian orders, consider the Serre quotients of their module categories with respect to pseudo-isomorphisms and describe injective objects in such quotient categories and its global homological dimension. These results generalize the results of I. Beck for the case of Krull rings. In particular, we establish the global homological dimension of the category of maximal Cohen-Macaulay modules over an order over a noetherian ring of Krull dimension 2.

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