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Displaying 41 – 60 of 72

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 $σ = (𝒯_{σ}, ℱ_{σ})$ is Goldie’s torsion theory and $ℱ_{σ}$ is a precover class, then $ℱ_{τ}$ is a precover class whenever...

Preradicals

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

Commentationes Mathematicae Universitatis Carolinae

Preradicals and change of rings

Ladislav Bican, Pavel Jambor, Tomáš Kepka, Petr Němec (1975)

Commentationes Mathematicae Universitatis Carolinae

Protolocalisations of exact Mal'cev categories.

Borceux, Francis, Gran, Marino, Mantovani, Sandra (2008)

Theory and Applications of Categories [electronic only]

Pseudohereditary and pseudocohereditary preradicals

Josef Jirásko (1979)

Commentationes Mathematicae Universitatis Carolinae

$Q F - 3^{'}$ modules and rings

Ladislav Bican (1973)

Commentationes Mathematicae Universitatis Carolinae

Quasi-radicals and Radicals in Categories

A. Buys, S. Veldsman (1985)

Publications de l'Institut Mathématique

Radicals which define factorization systems

Barry J. Gardner (1991)

Commentationes Mathematicae Universitatis Carolinae

A method due to Fay and Walls for associating a factorization system with a radical is examined for associative rings. It is shown that a factorization system results if and only if the radical is strict and supernilpotent. For groups and non-associative rings, no radical defines a factorization system.

Relative purity over Noetherian rings

Ladislav Bican (2007)

Mathematica Slovaca

Relatively exact modules

Ladislav Bican (2003)

Commentationes Mathematicae Universitatis Carolinae

Rim and Teply [10] investigated relatively exact modules in connection with the existence of torsionfree covers. In this note we shall study some properties of the lattice $ℰ_{τ} (M)$ of submodules of a torsionfree module $M$ consisting of all submodules $N$ of $M$ such that $M / N$ is torsionfree and such that every torsionfree homomorphic image of the relative injective hull of $M / N$ is relatively injective. The results obtained are applied to the study of relatively exact covers of torsionfree modules. As an application...