Xiao, Guangshi; Yin, Xiaobin; Tong, Wenting A note on AP-injective rings. (English) Zbl 1055.16004 J. Math. Res. Expo. 23, No. 2, 211-216 (2003). 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. Reviewer: Toma Albu (Istanbul) Cited in 1 Document MSC: 16D50 Injective modules, self-injective associative rings 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) Keywords:AP-injective rings; weakly injective rings; PP-rings; regular rings PDFBibTeX XMLCite \textit{G. Xiao} et al., J. Math. Res. Expo. 23, No. 2, 211--216 (2003; Zbl 1055.16004)