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On weakly f-clean rings
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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.
Title: On weakly f-clean rings
Description:
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.
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