# Non-singular covers over ordered monoid rings

Mathematica Bohemica (2006)

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

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topBican, 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 -

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