On torsion Gorenstein injective modules. (English) Zbl 0972.16001

The author continues to study Gorenstein rings and modules. He investigates what he calls Gorenstein injective rings, Gorenstein injective modules and injective envelopes of them. He characterizes Gorenstein injective modules. In the second part of the paper the crucial theorems assert, for a Gorenstein integral domain \(D\), a left \(D\)-module \(M\) and the Gorenstein injective envelope \(GM\) of \(M\), first that if \(D\) is injective and \(M\) is torsion then \(GM\) is also torsion, and secondly that the torsion submodule \(tGM\) of \(GM\) is Gorenstein injective. Moreover, it is proved that the property of being Gorenstein injective is preserved under direct limits.
Reviewer: Jan Paseka (Brno)


16D50 Injective modules, self-injective associative rings
13C12 Torsion modules and ideals in commutative rings
13C11 Injective and flat modules and ideals in commutative rings
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
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