Modules whose t-closed submodules are their homomorphic images

Abstract

In this paper, we introduce the notion of t-epi-modules. An R-module M is called t-epi if every t-closed submodule of M is a homomorphic image of M. Various properties of these modules are studied. Also, connections between t-epi modules and other related modules are investigated. Finally, quasi-Frobenius rings, right t-semi-simple rings and right S-t-extending rings are characterized in termes of t-epi modules.

Subject Classification:

• 16D10
• 16D40
• 16D60
• 16L30

Keywords:

• t-epi modules
• t-closed submodules
• epi-retractable modules
• Regular endomorphisms ring
• Nonsingular modules