Let R be an associative ring with an endomorphism σ and F ∪ {0}
the free monoid generated by U = {u1, . . . , ut} with 0 added, and M a factor
of F setting certain monomial in U to 0, enough so that, for some n, Mn = 0.
Then we can form the skew monoid ring R[M; σ]. An element of a ring R is
strongly clean if it is the sum of an idempotent and a unit that commute. In
this paper, we prove that P
g∈M rgg ∈ R[M; σ] is a strongly clean element, if
re or 1 − re is strongly π-regular in R. As a corollary, we deduce that if R is a
strongly π-regular ring, then the skew monoid ring R[M; σ] is strongly clean.
These rings is a new family of non-semiprime strongly clean skew monoid rings.
Konular | Matematik |
---|---|
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 17 Ocak 2017 |
Yayımlandığı Sayı | Yıl 2017 Cilt: 21 Sayı: 21 |