AGQP-injective modules

Abstract

Let R be a ring and let M be a right R-module with S = End(MR). M is called almost general quasi-principally injective (or AGQP-injective for short) if, for any 0 ≠ s ∈ S, there exist a positive integer n and a left ideal Xsn of S such that sn ≠ 0 and lS (Ker(sn)) = Ssn ⊕ Xsn. Some characterizations and properties of AGQP-injective modules are given, and some properties of AGQP-injective modules with additional conditions are studied.