| Title:
|
Non-singular covers over monoid rings (English) |
| Author:
|
Bican, Ladislav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
9-17 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We shall introduce the class of strongly cancellative multiplicative monoids which contains the class of all totally ordered cancellative monoids and it is contained in the class of all cancellative monoids. If $G$ is a strongly cancellative monoid such that $hG\subseteq Gh$ for each $h\in G$ and if $R$ is a ring such that $aR\subseteq Ra$ for each $a\in R$, then the class of all non-singular left $R$-modules is a cover class if and only if the class of all non-singular left $RG$-modules is a cover class. These two conditions are also equivalent whenever we replace the strongly cancellative monoid $G$ by the totally ordered cancellative monoid or by the totally ordered group. (English) |
| Keyword:
|
hereditary torsion theory |
| Keyword:
|
torsion theory of finite type |
| Keyword:
|
Goldie’s torsion theory |
| Keyword:
|
non-singular module |
| Keyword:
|
non-singular ring |
| Keyword:
|
monoid ring |
| Keyword:
|
precover class |
| Keyword:
|
cover class |
| MSC:
|
06F05 |
| MSC:
|
16D50 |
| MSC:
|
16D80 |
| MSC:
|
16S36 |
| MSC:
|
16S90 |
| MSC:
|
18E40 |
| idZBL:
|
Zbl 1170.16022 |
| idMR:
|
MR2400147 |
| DOI:
|
10.21136/MB.2008.133940 |
| . |
| Date available:
|
2009-09-24T22:33:51Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133940 |
| . |
| Reference:
|
[1] F. W. Anderson, K. R. Fuller: Rings and Categories of Modules.Graduate Texts in Mathematics 13, Springer, 1974. MR 1245487 |
| Reference:
|
[2] L. Bican: Torsionfree precovers.Contributions to General Algebra 15, Proceedings of the 66th Workshop on General Algebra, Klagenfurt 2003, Verlag Johannes Heyn, Klagenfurt, 2004, pp. 1–6. Zbl 1074.16002, MR 2080845 |
| Reference:
|
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| Reference:
|
[4] L. Bican: On torsionfree classes which are not precover classes.(to appear). Zbl 1166.16013, MR 2411109 |
| Reference:
|
[5] L. Bican: Non-singular precovers over polynomial rings.Comment. Math. Univ. Carol. 47 (2006), 369–377. Zbl 1106.16032, MR 2281000 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[13] M. L. Teply: Torsion-free covers II.Israel J. Math. 23 (1976), 132–136. Zbl 0321.16014, MR 0417245 |
| Reference:
|
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| Reference:
|
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| . |
