关于次希尔伯特代数的拟变分

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-04-16 DOI:10.1016/j.fss.2025.109418

Hernán Javier San Martín

{"title":"关于次希尔伯特代数的拟变分","authors":"Hernán Javier San Martín","doi":"10.1016/j.fss.2025.109418","DOIUrl":null,"url":null,"abstract":"<div><div>It is known that sub-Hilbert algebras are the implicative subreducts of subresiduated lattices. In this paper we give a new proof of this result by using some ideas employed to the study of the implicative-infimum subreducts of weak Heyting algebras. We also introduce open implicative filters in order to study the lattice of relative congruences of sub-Hilbert algebras. In particular, we introduce and study irreducible open implicative filters and we use this kind of open implicative filters in order to study the quasivariety of sub-Hilbert algebras generated by the class of its totally ordered members. Finally, we study a quasivariety which properly contains the variety of order Hilbert algebras.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"515 ","pages":"Article 109418"},"PeriodicalIF":3.2000,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the quasivariety of sub-Hilbert algebras\",\"authors\":\"Hernán Javier San Martín\",\"doi\":\"10.1016/j.fss.2025.109418\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>It is known that sub-Hilbert algebras are the implicative subreducts of subresiduated lattices. In this paper we give a new proof of this result by using some ideas employed to the study of the implicative-infimum subreducts of weak Heyting algebras. We also introduce open implicative filters in order to study the lattice of relative congruences of sub-Hilbert algebras. In particular, we introduce and study irreducible open implicative filters and we use this kind of open implicative filters in order to study the quasivariety of sub-Hilbert algebras generated by the class of its totally ordered members. Finally, we study a quasivariety which properly contains the variety of order Hilbert algebras.</div></div>\",\"PeriodicalId\":55130,\"journal\":{\"name\":\"Fuzzy Sets and Systems\",\"volume\":\"515 \",\"pages\":\"Article 109418\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2025-04-16\",\"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/S0165011425001575\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165011425001575","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

摘要

众所周知，亚希尔伯特代数是亚残差格的蕴涵子归结。在本文中，我们利用研究弱海尔丁代数的蕴含-最小子归结的一些思想，对这一结果给出了新的证明。我们还引入了开放蕴涵滤波器，以研究子希尔伯特代数的相对同调晶格。特别是，我们引入并研究了不可还原的开放蕴涵滤波器，并利用这类开放蕴涵滤波器来研究由其完全有序成员类生成的子希尔伯特代数的准变量。最后，我们研究了一个适当包含阶希尔伯特数的类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the quasivariety of sub-Hilbert algebras

It is known that sub-Hilbert algebras are the implicative subreducts of subresiduated lattices. In this paper we give a new proof of this result by using some ideas employed to the study of the implicative-infimum subreducts of weak Heyting algebras. We also introduce open implicative filters in order to study the lattice of relative congruences of sub-Hilbert algebras. In particular, we introduce and study irreducible open implicative filters and we use this kind of open implicative filters in order to study the quasivariety of sub-Hilbert algebras generated by the class of its totally ordered members. Finally, we study a quasivariety which properly contains the variety of order Hilbert algebras.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

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.