| Title:
|
On torsion Gorenstein injective modules (English) |
| Author:
|
Yi, Okyeon |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
445-454 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Nilpotent |
| Keyword:
|
Gorenstein Injective Modules |
| MSC:
|
13C11 |
| MSC:
|
13C12 |
| MSC:
|
13H10 |
| MSC:
|
16D50 |
| idZBL:
|
Zbl 0972.16001 |
| idMR:
|
MR1679639 |
| . |
| Date available:
|
2009-02-17T10:15:54Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107672 |
| . |
| Reference:
|
[1] Bass H.: On the ubiquity of Gorenstein rings.Math. Z. 82(1963), 8-28. Zbl 0112.26604, MR 0153708 |
| Reference:
|
[2] Enochs E.: Injective and flat covers, envelopes and resolvents.Israel J of Math. 39(1981), 189-209. Zbl 0464.16019, MR 0636889 |
| Reference:
|
[3] Enochs E., Jenda O. M. G.: Gorenstein injective and projective modules.Math. Z. 220(1995), 611-633. Zbl 0845.16005, MR 1363858 |
| Reference:
|
[4] Enochs E., Jenda O., Xu J.: Covers and envelopes over Gorenstein rings.(to appear in Tsukuba J. Math.) Zbl 0895.16001, MR 1422636 |
| Reference:
|
[5] Yasuo Iwanaga: On rings with finite self-injective dimension.Comm. Algebra, 7(4), (1979), 393-414. MR 0522552 |
| Reference:
|
[6] Yasuo Iwanaga: On rings with finite self-injective dimension II.Tsukuba J. Math. 4(1980), 107-113. MR 0597688 |
| Reference:
|
[7] Rotman J.: An introduction to homological algebra.Academic Press Inc., New York, 1979. Zbl 0441.18018, MR 0538169 |
| . |
