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- W2887404795 abstract "A *-ring R is strongly 2-nil-*-clean if every element in R is the sum of two projections and a nilpotent that commute. Fundamental properties of such *-rings are obtained. We prove that a *-ring R is strongly 2-nil-*-clean if and only if for all a ∈ R, a2 ∈ R is strongly nil-*-clean, if and only if for any a ∈ R there exists a *-tripotent e ∈ R such that a − e ∈ R is nilpotent and ea = ae, if and only if R is a strongly *-clean SN ring, if and only if R is abelian, J(R) is nil and R/J(R) is *-tripotent. Furthermore, we explore the structure of such rings and prove that a *-ring R is strongly 2-nil-*-clean if and only if R is abelian and R ≅ R1,R2 or R1 × R2, where R1/J(R1) is a *-Boolean ring and J(R1) is nil, R2/J(R2) is a *-Yaqub ring and J(R2) is nil. The uniqueness of projections of such rings are thereby investigated." @default.
- W2887404795 created "2018-08-22" @default.
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- W2887404795 creator A5031015351 @default.
- W2887404795 date "2018-08-06" @default.
- W2887404795 modified "2023-10-14" @default.
- W2887404795 title "Strongly 2-nil-clean rings with involutions" @default.
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- W2887404795 doi "https://doi.org/10.21136/cmj.2018.0291-17" @default.
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