Matrices over Zhou nil-clean rings

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 provide a large class of rings...

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Bibliographic Details
Published inCommunications in algebra Vol. 46; no. 4; pp. 1527 - 1533
Main Authors Abdolyousefi, Marjan Sheibani, Chen, Huanyin
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis Ltd 03.04.2018
Subjects
Rings (mathematics)
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Summary: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 provide a large class of rings over which every square matrix has such decompositions by tripotent and nilpotent matrices.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2017.1347666