{"title":"环中中心子的一般化","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":"{\"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}","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
摘要
让 R 是一个环，I 是 R 的一个非零理想，P 是 R 的一个素理想。在本文中，我们定义并研究了一类更普遍的中心子，我们称之为 I 中心子。此外，我们还研究了涉及两个 P 左中心子行为的代数等式，并得到了环 R/P 的换元准则或对所考虑的 P 左中心子的完整描述。
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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