MATHEMATICA BOHEMICA, Vol. 131, No. 1, pp. 95-104, 2006

Non-singular covers over ordered monoid rings

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 (MSC 2000): 16S90, 18E40, 16D80


Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.


[Previous Article] [Next Article] [Contents of This Number] [Contents of Mathematica Bohemica]
[Full text of the older issues of Mathematica Bohemica at DML-CZ]