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arXiv · 1702.08049

Matrices over Zhou nil-clean rings

Marjan Sheibani Abdolyousefi·Huanyin Chen
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Abstract

A ring R is Zhou nil-clean if every element in R is the sum of two tripotents and a nilpotent that commute. Let R be a Zhou nil-clean ring. If R is 2-primal (of bounded index), we prove that every square matrix over R is the sum of two tripotents and a nilpotent. These provides a large class of rings over which every square matrix has such decompositions by tripotent and nilpotent matrices.

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Marjan Sheibani Abdolyousefi, Huanyin Chen. 2017-02-26. Matrices over Zhou nil-clean rings. https://arxiv.org/abs/1702.08049

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