Matrices over Zhou nil-clean rings
Rings and Algebras
2017-02-28 v1
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.
Cite
@article{arxiv.1702.08049,
title = {Matrices over Zhou nil-clean rings},
author = {Marjan Sheibani Abdolyousefi and Huanyin Chen},
journal= {arXiv preprint arXiv:1702.08049},
year = {2017}
}