{"title":"Study of MV-algebras in view of R-ideals and 2R-ideals","authors":"Asiyeh Hassani Movahed , Mahta Bedrood , Arsham Borumand Saeid","doi":"10.1016/j.fss.2025.109313","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we introduce the concepts of <em>R</em>-ideal and 2<em>R</em>-ideal in <em>MV</em>-algebras. We explore various properties of these ideals and utilize them to characterize specific classes of <em>MV</em>-algebras, including <em>MV</em>-chains, (local, semisimple) <em>MV</em>-algebras. We clarify the relationships between <em>R</em>-ideals and 2<em>R</em>-ideals, and other types of ideals such as prime, primary, maximal and principal ideals. Finally, <span><math><msub><mrow><mo>∧</mo></mrow><mrow><mi>R</mi></mrow></msub></math></span>-multiplicatively closed system is defined and its relationship with <em>R</em>-ideals is examined.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"508 ","pages":"Article 109313"},"PeriodicalIF":3.2000,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165011425000521","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we introduce the concepts of R-ideal and 2R-ideal in MV-algebras. We explore various properties of these ideals and utilize them to characterize specific classes of MV-algebras, including MV-chains, (local, semisimple) MV-algebras. We clarify the relationships between R-ideals and 2R-ideals, and other types of ideals such as prime, primary, maximal and principal ideals. Finally, -multiplicatively closed system is defined and its relationship with R-ideals is examined.
期刊介绍：
Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies.
In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.
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