On torsion Gorenstein injective modules

Okyeon Yi

Archivum Mathematicum (1998)

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

Abstract

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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.

How to cite

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Yi, 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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  1. Bass H., On the ubiquity of Gorenstein rings, Math. Z. 82(1963), 8-28. (1963) Zbl0112.26604MR0153708
  2. Enochs E., Injective and flat covers, envelopes and resolvents, Israel J of Math. 39(1981), 189-209. (1981) Zbl0464.16019MR0636889
  3. Enochs E., Jenda O. M. G., Gorenstein injective and projective modules, Math. Z. 220(1995), 611-633. (1995) Zbl0845.16005MR1363858
  4. Enochs E., Jenda O., Xu J., Covers and envelopes over Gorenstein rings, (to appear in Tsukuba J. Math.) Zbl0895.16001MR1422636
  5. Yasuo Iwanaga, On rings with finite self-injective dimension, Comm. Algebra, 7(4), (1979), 393-414. (1979) MR0522552
  6. Yasuo Iwanaga, On rings with finite self-injective dimension II, Tsukuba J. Math. 4(1980), 107-113. (1980) MR0597688
  7. Rotman J., An introduction to homological algebra, Academic Press Inc., New York, 1979. (1979) Zbl0441.18018MR0538169

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