{"title":"A non-commutative generalization of Łukasiewicz rings","authors":"Albert Kadji , Celestin Lele , Jean B. Nganou","doi":"10.1016/j.jal.2016.04.001","DOIUrl":null,"url":null,"abstract":"<div><p>The goal of the present article is to extend the study of commutative rings whose ideals form an MV-algebra as carried out by Belluce and Di Nola <span>[1]</span> to non-commutative rings. We study and characterize all rings whose ideals form a pseudo MV-algebra, which shall be called here generalized Łukasiewicz rings. We obtain that these are (up to isomorphism) exactly the direct sums of unitary special primary rings.</p></div>","PeriodicalId":54881,"journal":{"name":"Journal of Applied Logic","volume":"16 ","pages":"Pages 1-13"},"PeriodicalIF":0.0000,"publicationDate":"2016-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jal.2016.04.001","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Logic","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1570868316300118","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
The goal of the present article is to extend the study of commutative rings whose ideals form an MV-algebra as carried out by Belluce and Di Nola [1] to non-commutative rings. We study and characterize all rings whose ideals form a pseudo MV-algebra, which shall be called here generalized Łukasiewicz rings. We obtain that these are (up to isomorphism) exactly the direct sums of unitary special primary rings.
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