Displaying similar documents to “Non-singular covers over ordered monoid rings”

Non-singular covers over monoid rings

Ladislav Bican (2008)

Mathematica Bohemica

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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 h G G h for each h G and if R is a ring such that a R R a for each a 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 R G -modules is a cover class. These two conditions are also...

Non-singular precovers over polynomial rings

Ladislav Bican (2006)

Commentationes Mathematicae Universitatis Carolinae

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One of the results in my previous paper , preprint, Corollary 3, states that for every hereditary torsion theory τ for the category R -mod with τ σ , σ being Goldie’s torsion theory, the class of all τ -torsionfree modules forms a (pre)cover class if and only if τ is of finite type. The purpose of this note is to show that all members of the countable set 𝔐 = { R , R / σ ( R ) , R [ x 1 , , x n ] , R [ x 1 , , x n ] / σ ( R [ x 1 , , x n ] ) , n < ω } of rings have the property that the class of all non-singular left modules forms a (pre)cover class if and only if this holds for an...

Precovers and Goldie’s torsion theory

Ladislav Bican (2003)

Mathematica Bohemica

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Recently, Rim and Teply , using the notion of τ -exact modules, found a necessary condition for the existence of τ -torsionfree covers with respect to a given hereditary torsion theory τ for the category R -mod of all unitary left R -modules over an associative ring R with identity. Some relations between τ -torsionfree and τ -exact covers have been investigated in . The purpose of this note is to show that if σ = ( 𝒯 σ , σ ) is Goldie’s torsion theory and σ is a precover class, then τ is a precover class...