U. Albrecht, Francisco Javier Santillán-Covarrubias
{"title":"A note on almost maximal chain rings","authors":"U. Albrecht, Francisco Javier Santillán-Covarrubias","doi":"10.4171/rsmup/52","DOIUrl":null,"url":null,"abstract":"This paper discusses maximal and almost maximal rings in a noncommutative setting. Annihilators ideals in chain rings and their relationship to the concept of self-injectivity are investigated. In particular, a two-sided chain ring is right self-injective if and only if it is right co-Hopfian and a left maximal ring. Finally, localizations of chain rings are discussed. Mathematics Subject Classification (2010). Primary 16L30; Secondary 16D50; 16P70","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"9 1","pages":"1-11"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/52","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
This paper discusses maximal and almost maximal rings in a noncommutative setting. Annihilators ideals in chain rings and their relationship to the concept of self-injectivity are investigated. In particular, a two-sided chain ring is right self-injective if and only if it is right co-Hopfian and a left maximal ring. Finally, localizations of chain rings are discussed. Mathematics Subject Classification (2010). Primary 16L30; Secondary 16D50; 16P70
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