Iso-retractability of modules related to small submodules

Year 2025, Early Access, 1 - 13

Nirbhay Kumar , Avanish Chaturvedi

https://doi.org/10.24330/ieja.1611483

Abstract

We study the notion of small iso-retractable modules. We prove that a small iso-retractable module is either $J$-semisimple or iso-retractable (iso-simple). Further, we prove that a ring $R$ is a left V-ring if and only if every left $R$-module is small iso-retractable. Also, we give a new characterization of semisimple modules in terms of small iso-retractable modules.

Keywords

Semisimple module, small submodule, iso-retractable module

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