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MATHEMATICA BOHEMICA, Vol. 131, No. 1, pp. 95-104 (2006)
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Non-singular covers over ordered monoid rings

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Ladislav Bican

* Ladislav Bican*, KA MFF UK, Sokolovska 83, 186 00 Praha 8-Karlin, Czech Republik, e-mail: ` bican@karlin.mff.cuni.cz`

**Abstract:** 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.

**Keywords:** hereditary torsion theory, torsion theory of finite type, Goldie's torsion theory, non-singular module, non-singular ring, monoid ring, precover class, cover class

**Classification (MSC2000):** 16S90, 18E40, 16D80

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