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- W2800941292 abstract "Let R be a ring with an endomorphism σ and F ∪ {0} the free monoid generated by U = { u 1 , ..., u t } with 0 added, and M = F ∪ {0}/( I ) where I is the set of certain monomial in U such that M n = 0, for some n . Then we can form the non-semiprime skew monoid ring R [ M ; σ]. An element a ∈ R is uniquely strongly clean if a has a unique expression as a = e + u , where e is an idempotent and u is a unit with ea = ae . We show that a σ-compatible ring R is uniquely clean if and only if R [ M ; σ] is a uniquely clean ring. If R is strongly π-regular and uniquely strongly clean, then R [ M ; σ] is uniquely strongly clean. It is also shown that idempotents of R [ M ; σ] (and hence the ring R [ x ; σ]=( x n )) are conjugate to idempotents of R and we apply this to show that R [ M ; σ] over a projective-free ring R is projective-free. It is also proved that if R is semi-abelian and σ( e ) = e for each idempotent e ∈ R , then R [ M ; σ] is a semi-abelian ring." @default.
- W2800941292 created "2018-05-17" @default.
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- W2800941292 date "2018-03-01" @default.
- W2800941292 modified "2023-09-27" @default.
- W2800941292 title "Idempotent elements and uniquely clean property of skew monoid rings" @default.
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- W2800941292 doi "https://doi.org/10.1556/012.2018.55.1.1376" @default.
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