Strongly J-Clean Rings with Involutions
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∈ R, there exists a unique projection e∈ R such that a-e is invertible and ae=ea.
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