Supplement Submodules of Injective Modules

Abstract

An R-module M is called almost injective if M is a supplement submodule of every module which contains M. The module M is called F-almost injective if every factor module of M is almost injective. It is shown that a ring R is a right H-ring if and only if R is right perfect and every almost injective module is injective. We prove that a ring R is semisimple if and only if the R-module R _R is F-almost injective.

Key Words:

• Almost injective modules
• F-almost injective modules
• Injective modules
• Lifting modules
• Noncosingular modules
• Small modules
• Weakly injective modules

2000 Mathematics Subject Classification:

• 16D50
• 16D99
• 16L30

Notes

Communicated by T. Albu.