Iso-retractable modules and rings

Abstract

The modules which are isomorphic to their non-zero submodules are known as iso-retractable. We characterize simple modules in terms of iso-retractable modules. We provide several sufficient conditions for iso-retractable modules to be simple. We show that if the endomorphism ring of an iso-retractable module is von-Neumann regular then [Formula: see text] is a simple module. In general, iso-retractable modules need not be projective (injective) and vice versa. We investigate some properties of iso-retractable modules with projectivity as well as injectivity. Finally, we provide some open problems.