On \(*\)-\(r\)-Clean Rings
DOI:
https://doi.org/10.26713/cma.v16i3.3126Keywords:
Involution, ∗-r-clean ring, ∗-clean ring, Ring extensionsAbstract
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.
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