1. Department of Mathematics and Statistics , Otago University , Dunedin, New Zealand;2. Département de Mathématiques , Faculté des Sciences de Tétouan , Tétouan, Morocco
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 RR is F-almost injective.