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A note on AP-injective rings. (English) Zbl 1055.16004

An associative ring \(R\) with identity element is said to be ‘AP-injective’ if for any \(a\in R\) there exists a left ideal \(X_a\) of \(R\) such that \(\ell r(a)=Ra\oplus X_a\). The aim of this note is to investigate this property of \(R\) in connection with the properties of \(R\) being regular, PP, self-injective, and/or weakly injective.

MSC:

16D50 Injective modules, self-injective associative rings
16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
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