| Title:
|
Non-singular covers over ordered monoid rings (English) |
| Author:
|
Bican, Ladislav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
95-104 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a multiplicative monoid. If $RG$ is a non-singular ring such that the class of all non-singular $RG$-modules is a cover class, then the class of all non-singular $R$-modules is a cover class. These two conditions are equivalent whenever $G$ is a well-ordered cancellative monoid such that for all elements $g,h\in G$ with $g < h$ there is $l\in G$ such that $lg = h$. For a totally ordered cancellative monoid the equalities $Z(RG) = Z(R)G$ and $\sigma (RG) = \sigma (R)G$ hold, $\sigma $ being Goldie’s torsion theory. (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 1111.16029 |
| idMR:
|
MR2211006 |
| DOI:
|
10.21136/MB.2006.134079 |
| . |
| Date available:
|
2009-09-24T22:24:37Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134079 |
| . |
| Reference:
|
[1] F. W. Anderson, K. R. Fuller: Rings and Categories of Modules.Graduate Texts in Mathematics, vol. 13, Springer, 1974. MR 0417223 |
| Reference:
|
[2] L. Bican: Torsionfree precovers.Proceedings of the Klagenfurt Conference 2003 (66. AAA), Verlag Johannes Heyn, Klagenfurt, 2004, pp. 1–6. Zbl 1074.16002, MR 2080845 |
| Reference:
|
[3] L. Bican: Precovers and Goldie’s torsion theory.Math. Bohem. 128 (2003), 395–400. Zbl 1057.16027, MR 2032476 |
| 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.(to appear). 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:
|
[10] J. Golan: Torsion Theories.Pitman Monographs and Surveys in Pure and Applied Matematics, 29, Longman Scientific and Technical, 1986. Zbl 0657.16017, MR 0880019 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[13] M. L. Teply: Some aspects of Goldie’s torsion theory.Pacif. J. Math. 29 (1969), 447–459. Zbl 0174.06803, MR 0244323, 10.2140/pjm.1969.29.447 |
| Reference:
|
[14] J. Xu: Flat Covers of Modules.Lecture Notes in Mathematics 1634, Springer, Berlin, 1996. Zbl 0860.16002, MR 1438789 |
| . |
