Almost MGP-injective rings. (English) Zbl 1311.16001

Ukr. Math. J. 65, No. 11, 1634-1641 (2014) and Ukr. Mat. Zh. 65, No. 11, 1476-1481 (2013).
Summary: A ring \(R\) is called right almost MGP-injective (or AMGP-injective) if, for any \(0\neq a\in R\), there exists an element \(b\in R\) such that \(ab=ba\neq 0\) 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 established 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.


16D50 Injective modules, self-injective associative rings
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