零清洁2 × 2积分矩阵的Jacobsons引理失效

Pub Date : 2020-12-01 DOI:10.2478/auom-2020-0035

G. Călugăreanu, Horia F. Pop

{"title":"零清洁2 × 2积分矩阵的Jacobsons引理失效","authors":"G. Călugăreanu, Horia F. Pop","doi":"10.2478/auom-2020-0035","DOIUrl":null,"url":null,"abstract":"Abstract We show that for two 2 × 2 integral matrices A, B, if the product AB is nil-clean then BA may not be nil-clean. Despite the fact that for many special cases, BA is also nil-clean, we finally found three counterexamples. All the way, the computer aid was decisive.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices\",\"authors\":\"G. Călugăreanu, Horia F. Pop\",\"doi\":\"10.2478/auom-2020-0035\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We show that for two 2 × 2 integral matrices A, B, if the product AB is nil-clean then BA may not be nil-clean. Despite the fact that for many special cases, BA is also nil-clean, we finally found three counterexamples. All the way, the computer aid was decisive.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2478/auom-2020-0035\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2478/auom-2020-0035","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文证明了对于两个2 × 2积分矩阵A, B，如果乘积AB是零清洁的，则BA可能不是零清洁的。尽管对于许多特殊情况，BA也是零干净的，但我们最终找到了三个反例。一直以来，计算机辅助都是决定性的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Jacobsons Lemma fails for nil-clean 2 × 2 integral matrices

Abstract We show that for two 2 × 2 integral matrices A, B, if the product AB is nil-clean then BA may not be nil-clean. Despite the fact that for many special cases, BA is also nil-clean, we finally found three counterexamples. All the way, the computer aid was decisive.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助