On \(*\)-\(r\)-Clean Rings - Ma, Guanglin (Communications in Mathematics and Applications, 2025)
A ring with an involution \(*\) is called \(*\)-\(r\)-clean if every element is a sum of a projection and a regular element (in the sense of von Neumann). In this article, several connections between \(*\)-\(r\)-clean rings and \(*\)-clean rings are given. Different characterizations of \(*\)-\(r\)-clean rings are presented. The passage of this property to some extensions of rings is studied.
Keywords: Involution; ∗-r-clean ring; ∗-clean ring; Ring extensions