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Strongly J-Clean Rings with Involutions (1207.0466v2)
Published 2 Jul 2012 in math.RA
Abstract: A ring with an involution * is called strongly $J$--clean if every element is a sum of a projection and an element of the Jacobson radical that commute. In this article, we prove several results characterizing this class of rings. It is shown that a *-ring $R$ is strongly $J$--clean, if and only if $R$ is uniquely clean and strongly *-clean, if and only if $R$ is uniquely strongly *-clean, that is, for any $a\in R$, there exists a unique projection $e\in R$ such that $a-e$ is invertible and $ae=ea$.
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