On FI-mono-retractable modules

[摘要] 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.

[学科分类] 物理化学和理论化学

[关键词] retractable module;FI-mono-retractable module;compressible module;fully invariant submodule