# On torsion Gorenstein injective modules

Archivum Mathematicum (1998)

- Volume: 034, Issue: 4, page 445-454
- ISSN: 0044-8753

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topYi, Okyeon. "On torsion Gorenstein injective modules." Archivum Mathematicum 034.4 (1998): 445-454. <http://eudml.org/doc/248191>.

@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 -

## References

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- Yasuo Iwanaga, On rings with finite self-injective dimension, Comm. Algebra, 7(4), (1979), 393-414. (1979) MR0522552
- Yasuo Iwanaga, On rings with finite self-injective dimension II, Tsukuba J. Math. 4(1980), 107-113. (1980) MR0597688
- Rotman J., An introduction to homological algebra, Academic Press Inc., New York, 1979. (1979) Zbl0441.18018MR0538169

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