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On torsion Gorenstein injective modules

Okyeon Yi — 1998

Archivum Mathematicum

In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if $D$ is a Gorenstein integral domain and $M$ is a left $D$ -module, then the torsion submodule $t G M$ of Gorenstein injective envelope $G M$ of $M$ is also Gorenstein injective. We can also show that if $M$ is a torsion $D$ -module of a Gorenstein injective integral domain $D$ , then the Gorenstein injective envelope $G M$ of $M$ is torsion.

On locally nilpotent endomorphisms of Gorenstein injective modules.

Yi, Okyeon — 1998

Southwest Journal of Pure and Applied Mathematics [electronic only]

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