A generalization of purely extending modules relative to a torsion theory

Year 2021, Volume: 70 Issue: 2, 1099 - 1112, 31.12.2021

Semra Doğruöz , Azime Tarhan

https://doi.org/10.31801/cfsuasmas.898637

Abstract

In this work we introduce a new concept, namely, ${\tau }_s$-extending modules (rings) which is torsion-theoretic analogues of extending modules and then we extend many results from extending modules to this new concept. For instance we show that for any ring $R$ with unit, if $_{R}R$ is purely ${\tau }_s$-extending if and only if every cyclic $\tau$-nonsingular $R$-module is flat. Also, we make a classification for the direct sums of the rings to be purely ${\tau }_s$-extending.

Keywords

Pure submodule, closed submodule, (non)singular module, extending module, torsion theory

Project Number

FEF-17041

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