AGQP-injective modules. (English) Zbl 1160.16002

Summary: Let \(R\) be a ring and let \(M\) be a right \(R\)-module with \(S=\text{End}(M_R)\). \(M\) is called ‘almost general quasi-principally injective’ (or AGQP-injective for short) if, for any \(0\neq s\in S\), there exist a positive integer \(n\) and a left ideal \(X_{s^n}\) of \(S\) such that \(s^n\neq 0\) and \(\mathbf l_S(\text{Ker}(s^n))=Ss^n\oplus X_{s^n}\). Some characterizations and properties of AGQP-injective modules are given, and some properties of AGQP-injective modules with additional conditions are studied.


16D50 Injective modules, self-injective associative rings


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