{"title":"A generalization of centralizers in rings","authors":"Lahcen Oukhtite, Karim Bouchannafa","doi":"10.1007/s11565-023-00478-1","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>R</i> be a ring, <i>I</i> a nonzero ideal of <i>R</i> and <i>P</i> a prime ideal of <i>R</i>. In this paper we define and study a more general class of centralizers that we call an <i>I</i>-centralizers. Moreover, we investigate algebraic identities involving the behavior of a two <i>P</i>-left centralizers and we either get a commutativity criterion for the ring <i>R</i>/<i>P</i> or a complete description of the considered a <i>P</i>-left centralizers.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 2","pages":"405 - 416"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali dell''Universita di Ferrara","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s11565-023-00478-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Let R be a ring, I a nonzero ideal of R and P a prime ideal of R. In this paper we define and study a more general class of centralizers that we call an I-centralizers. Moreover, we investigate algebraic identities involving the behavior of a two P-left centralizers and we either get a commutativity criterion for the ring R/P or a complete description of the considered a P-left centralizers.
期刊介绍：
Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.
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