Mbarek Zaoui, Driss Gretete, El Mustapha El Abbassi, Brahim Fahid
{"title":"Symmetric bi-derivations of residuated lattices","authors":"Mbarek Zaoui, Driss Gretete, El Mustapha El Abbassi, Brahim Fahid","doi":"10.1007/s11565-023-00468-3","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we introduced the notion of symmetric bi-derivations on residuated lattices and investigated some related properties. Some relationships between symmetric bi-derivation and <i>k</i>-isotone, <i>k</i>-contractive and <i>k</i>-ideal symmetric bi-derivations are given. Also, we introduce the sets of <i>k</i>-fixed points of a symmetric bi-derivation and its structure is studied. In particular, we show that the “family” of sets of <i>k</i>-fixed points forms a residuated lattice.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 2","pages":"235 - 248"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-19","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/s11565-023-00468-3","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
In this paper, we introduced the notion of symmetric bi-derivations on residuated lattices and investigated some related properties. Some relationships between symmetric bi-derivation and k-isotone, k-contractive and k-ideal symmetric bi-derivations are given. Also, we introduce the sets of k-fixed points of a symmetric bi-derivation and its structure is studied. In particular, we show that the “family” of sets of k-fixed points forms a residuated lattice.
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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