{"title":"3×3 idempotent matrices over some domains and a conjecture on nil-clean matrices","authors":"G. Călugăreanu","doi":"10.47743/anstim.2022.00007","DOIUrl":null,"url":null,"abstract":"A characterization of the 3 × 3 idempotent matrices over some integral domains is given, in terms of determinant, trace and rank. The conjecture: every nil-clean 3 × 3 integral matrix is exchange, is revisited. Several new cases are proved.","PeriodicalId":55523,"journal":{"name":"Analele Stiintifice Ale Universitatii Al I Cuza Din Iasi - Matematica","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analele Stiintifice Ale Universitatii Al I Cuza Din Iasi - Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47743/anstim.2022.00007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
A characterization of the 3 × 3 idempotent matrices over some integral domains is given, in terms of determinant, trace and rank. The conjecture: every nil-clean 3 × 3 integral matrix is exchange, is revisited. Several new cases are proved.
期刊介绍：
This journal is devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research and research-expository papers in all fields of mathematics.
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