Displaying similar documents to “Hereditary tensor-orthogonal theories”

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...