Displaying similar documents to “Non-singular precovers over polynomial rings”

Non-singular covers over ordered monoid rings

Ladislav Bican (2006)

Mathematica Bohemica

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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.

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...

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 , ℱ σ ) is Goldie’s torsion theory and ℱ σ is a precover class, then ℱ τ is a precover class...