{"title":"Some results on derivations of MV-algebras","authors":"Jun-tao Wang, Peng-fei He, Yan-hong She","doi":"10.1007/s11766-023-4054-8","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we review some of their related properties of derivations on MV-algebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic. In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive (implicative) derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, <b>303</b>(2016), 97–113] and [Information Sciences, <b>178</b>(2008), 307–316].</p></div>","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":"38 1","pages":"126 - 143"},"PeriodicalIF":1.0000,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11766-023-4054-8.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-023-4054-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we review some of their related properties of derivations on MV-algebras and give some characterizations of additive derivations. Then we prove that the fixed point set of Boolean additive derivations and that of their adjoint derivations are isomorphic. In particular, we prove that every MV-algebra is isomorphic to the direct product of the fixed point set of Boolean additive derivations and that of their adjoint derivations. Finally we show that every Boolean algebra is isomorphic to the algebra of all Boolean additive (implicative) derivations. These results also give the negative answers to two open problems, which were proposed in [Fuzzy Sets and Systems, 303(2016), 97–113] and [Information Sciences, 178(2008), 307–316].
期刊介绍：
Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects.
The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry.
Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.
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