A generalization of purely extending modules relative to a torsion theory
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Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Universitesi
Abstract
In this work we introduce a new concept, namely,
τ
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
τ
s
-extending if and only if every cyclic
τ
-nonsingular
R
-module is flat. Also, we make a classification for the direct sums of the rings to be purely
τ
s
-extending.
Description
Keywords
Pure submodule, closed submodule, (non)singular module, extending module, torsion theory