A generalization of purely extending modules relative to a torsion theory

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:70 Issue:2
A generalization of purely extending modules relative to a torsion theory

A generalization of purely extending modules relative to a torsion theory

Authors : Semra DOĞRUÖZ, Azime TARHAN

Pages : 1099-1112

Doi:10.31801/cfsuasmas.898637

View : 14 | Download : 12

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :In this work we introduce a new concept, namely, τ s τs -extending modules insert ignore into journalissuearticles values(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 R with unit, if $_{R}R$ R is purely τ s τs -extending if and only if every cyclic τ τ -nonsingular R R -module is flat. Also, we make a classification for the direct sums of the rings to be purely τ s τs -extending.
Keywords : Pure submodule, closed submodule non, singular module, extending module, torsion theory

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