AGQP-injective modules. Let R be a ring and let M be a right R-module with S=End(M R ). 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 X s n of S such that s n ≠0 and 𝐥 S (Ker(s n ))=Ss n ⊕X s n . Some characterizations and properties of AGQP-injective modules are given, and some properties of AGQP-injective modules with additional conditions are studied.
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