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Keywords:
retractable module; FI-mono-retractable module; compressible module; fully invariant submodule
retractable module; FI-mono-retractable module; compressible module; fully invariant submodule
Summary:
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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