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Non-singular precovers over polynomial rings

Ladislav Bican (2006)

Commentationes Mathematicae Universitatis Carolinae

One of the results in my previous paper On torsionfree classes which are not precover classes, 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...

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