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On FI-mono-retractable modules

Marziyeh Atashkar;  Yahya Talebi — 2022

Commentationes Mathematicae Universitatis Carolinae

We introduce the notion of FI-mono-retractable modules which is a generalization of compressible modules. We investigate the properties of such modules. It is shown that the rings over which every cyclic module is FI-mono-retractable are simple Noetherian V -ring with zero socle or Artinian semisimple. The last section of the paper is devoted to the endomorphism rings of FI-retractable modules.

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