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Precobalanced and cobalanced sequences of modules over domains

Anthony Giovannitti, H. Pat Goeters (2007)

Mathematica Bohemica

The class of pure submodules ( 𝒫 ) and torsion-free images ( ) of finite direct sums of submodules of the quotient field of an integral domain were first investigated by M. C. R. Butler for the ring of integers (1965). In this case 𝒫 = and short exact sequences of such modules are both prebalanced and precobalanced. This does not hold for integral domains in general. In this paper the notion of precobalanced sequences of modules is further investigated. It is shown that as in the case for abelian groups...

Precovers and Goldie’s torsion theory

Ladislav Bican (2003)

Mathematica Bohemica

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 whenever...

Preradicals

Ladislav Bican, Pavel Jambor, Tomáš Kepka, Petr Němec (1974)

Commentationes Mathematicae Universitatis Carolinae

Proarrows II

R. J. Wood (1985)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Product preserving bundle functors on fibered fibered manifolds

Włodzimierz M. Mikulski, Jiří M. Tomáš (2003)

Colloquium Mathematicae

We investigate the category of product preserving bundle functors defined on the category of fibered fibered manifolds. We show a bijective correspondence between this category and a certain category of commutative diagrams on product preserving bundle functors defined on the category ℳ f of smooth manifolds. By an application of the theory of Weil functors, the latter category is considered as a category of commutative diagrams on Weil algebras. We also mention the relation with natural transformations...

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