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A subclass of strongly clean rings

Orhan Gurgun;  Sait Halicioglu and Burcu Ungor — 2015

Communications in Mathematics

In this paper, we introduce a subclass of strongly clean rings. Let R be a ring with identity, J be the Jacobson radical of R , and let J # denote the set of all elements of R which are nilpotent in R / J . An element a ∈ R is called provided that there exists an idempotent e ∈ R such that a e = e a and a - e or a + e is an element of J # . A ring R is said to be in case every element in R is very J # -clean. We prove that every very J # -clean ring is strongly π -rad clean and has stable range one. It is shown that for a commutative...

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