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- W2095385979 abstract "A $*$-ring $R$ is called (strongly) $*$-clean if every element of $R$ is the sum of a projection and a unit (which commute with each other). In this note, some properties of $*$-clean rings are considered. In particular, a new class of $*$-clean rings which called strongly $pi$-$*$-regular are introduced. It is shown that $R$ is strongly $pi$-$*$-regular if and only if $R$ is $pi$-regular and every idempotent of $R$ is a projection if and only if $R/J(R)$ is strongly regular with $J(R)$ nil, and every idempotent of $R/J(R)$ is lifted to a central projection of $R.$ In addition, the stable range conditions of $*$-clean rings are discussed, and equivalent conditions among $*$-rings related to $*$-cleanness are obtained." @default.
- W2095385979 created "2016-06-24" @default.
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- W2095385979 date "2015-01-13" @default.
- W2095385979 modified "2023-09-27" @default.
- W2095385979 title "A Note on $*$-Clean Rings" @default.
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