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arXiv · 1705.05094

On Zhou nil-clean rings

Marjan Sheibani Abdolyousefi·Nahid Ashrafi·Huanyin Chen
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Abstract

A ring R is a Zhou nil-clean ring if every element in R is the sum of two tripotents and a nilpotent that commute. In this paper, Zhou nil-clean rings are further discussed with an emphasis on their relations with polynomials, idempotents and 2- idempotents. any a \in R, there exists e 2 Z[a] such that a-e \in R is nilpotent and e^5 = 5e^3 -4e, if and only if for any a 2 R, there exist idempotents e; f; g; h 2 Z[a] and a nilpotent w such that a = e+f +g+h+w, if and only if for any a 2 R, there exist 2-idempotents e; f 2 Z[a] and a nilpotent w 2 R such that a = e + f + w, if and only if for any a 2 R, there exists a 2-idempotent e 2 Z[a] and a nilpotent w 2 R such that a^2 = e+w, if and only if R is a Kosan exchange ring.

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Marjan Sheibani Abdolyousefi, Nahid Ashrafi, Huanyin Chen. 2017-05-15. On Zhou nil-clean rings. https://arxiv.org/abs/1705.05094

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