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On Gorenstein injective modules. (English) Zbl 0783.13011

Dualizing the classical notions of injective envelope and projective cover, the authors in previous papers have set up an extensive theory of injective covers and projective envelopes available for certain classes of modules. Using injective covers, one can obtain a minimal-degree-wise injective complex resolving a module, \(M\) (called the minimal injective resolvent of \(M\)). The module \(M\) is said to be Gorenstein injective if some injective resolvent of \(M\) is an injective resolution and some injective resolution of \(M\) is an injective resolvent. (Dually one obtains a notion of Gorenstein projective module.) This paper explores in some depth characterizations of Gorenstein injective modules over various types of rings.
Reviewer: T.Porter (Bangor)

MSC:

13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
13C11 Injective and flat modules and ideals in commutative rings
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