On weakly f-clean rings

Let R be an associative ring with identity and Id(R) and K(R) denote the set of idempotents and full elements of R respectively. The notion of weakly f-clean rings where element r can be written as r = f + e or r = f − e, e ∈ Id(R) and f ∈ K(R) was introduced. Different properties of weakly f-clean rings were studied. It was shown that a left quasi-duo ring R is weakly clean if and only if R is a weakly f-clean ring. Finally, it was shown that the ring of skew Hurwitz series T = (HR, α) where α is an automorphism of R is weakly f-clean if and only if R is weakly f-clean.