Non-singular covers over ordered monoid rings

Ladislav Bican

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 1, page 95-104
  • ISSN: 0862-7959

Abstract

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Let G be a multiplicative monoid. If R G is a non-singular ring such that the class of all non-singular R G -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 ∈ G with g < h there is l ∈ G such that l g = h . For a totally ordered cancellative monoid the equalities Z ( R G ) = Z ( R ) G and σ ( R G ) = σ ( R ) G hold, σ being Goldie’s torsion theory.

How to cite

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Bican, Ladislav. "Non-singular covers over ordered monoid rings." Mathematica Bohemica 131.1 (2006): 95-104. <http://eudml.org/doc/249912>.

@article{Bican2006,
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.},
author = {Bican, Ladislav},
journal = {Mathematica Bohemica},
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; hereditary torsion theories; torsion theories of finite type; Goldie torsion theory; non-singular modules; non-singular rings; precover classes; cover classes; semigroup rings},
language = {eng},
number = {1},
pages = {95-104},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non-singular covers over ordered monoid rings},
url = {http://eudml.org/doc/249912},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Bican, Ladislav
TI - Non-singular covers over ordered monoid rings
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 1
SP - 95
EP - 104
AB - 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.
LA - eng
KW - hereditary torsion theory; torsion theory of finite type; Goldie’s torsion theory; non-singular module; non-singular ring; monoid ring; precover class; cover class; hereditary torsion theories; torsion theories of finite type; Goldie torsion theory; non-singular modules; non-singular rings; precover classes; cover classes; semigroup rings
UR - http://eudml.org/doc/249912
ER -

References

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