Almost MGP-Injective Rings

Abstract

A ring R is called right almost MGP-injective (or AMGP-injective) if, for any 0 ≠ a ∈ R, there exists an element b ∈ R such that ab = ba ≠ 0 and any right R-monomorphism from abR to R can be extended to an endomorphism of R. In the paper, several properties of these rings are establshed and some interesting results are obtained. By using the concept of right AMGP-injective rings, we present some new characterizations of QF-rings, semisimple Artinian rings, and simple Artinian rings.