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Research articles

Pretorsions in modules and associated closure operators

A. I. Kashu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., Chişinău, MD-2028 Moldova

Abstract: This article contains the results on the pretorsions of the module category $R$-Mod and on the closure operators defined by them. The pretorsions of $R$-Mod can be described in diverse forms: by classes of modules, filters of left ideals of $R$, closure operators, dense submodules, etc. In the set $\mathbb{PT}$ of pretorsions of $R$-Mod the main operations are studied, as well as their expressions in terms of classes of modules, filters, operators, etc. The approximations of pretorsions by jansian pretorsions and by torsions are mentioned.

Keywords and phrases: pretorsion, torsion, closure operator, (pre)radical filter, torsion class, torsionfree class, jansian pretorsion.

MSC: 16D90, 16S90, 06B23

Received: 26.05.2016

Language: English

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