Duality Between Injective Envelopes and Flat Covers over Noether Algebras
Xiaolei Zhang
Abstract
It follows by Puuska that, over a commutative Noetherian ring R, a morphism i : M → I of R-modules is an injective envelope if and only if its Matlis dual HomR(i, E) is a flat cover for some injective cogenerator E, and equivalently for every injective R-module E. In this paper, we will generalize this result to non-commutative Noetherian algebras.
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