Abstract: 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.
Keywords: retractable module; FI-mono-retractable module; compressible module; fully invariant submodule
DOI: DOI 10.14712/1213-7243.2022.019
AMS Subject Classification: 16D10 16D80