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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:
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