On torsion Gorenstein injective modules

@article{Yi1998,
abstract = {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 $tGM$ of Gorenstein injective envelope $GM$ 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 $GM$ of $M$ is torsion.},
author = {Yi, Okyeon},
journal = {Archivum Mathematicum},
keywords = {Nilpotent; Gorenstein Injective Modules; Gorenstein injective rings; Gorenstein injective modules; torsion modules; injective hulls},
language = {eng},
number = {4},
pages = {445-454},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On torsion Gorenstein injective modules},
url = {http://eudml.org/doc/248191},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Yi, Okyeon
TI - On torsion Gorenstein injective modules
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 4
SP - 445
EP - 454
AB - 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 $tGM$ of Gorenstein injective envelope $GM$ 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 $GM$ of $M$ is torsion.
LA - eng
KW - Nilpotent; Gorenstein Injective Modules; Gorenstein injective rings; Gorenstein injective modules; torsion modules; injective hulls
UR - http://eudml.org/doc/248191
ER -