{"title":"On z-elements of multiplicative lattices","authors":"Amartya Goswami, Themba Dube","doi":"10.1007/s00012-024-00882-4","DOIUrl":null,"url":null,"abstract":"<div><p>The aim of this paper is to investigate further properties of <i>z</i>-elements in multiplicative lattices. We utilize <i>z</i>-closure operators to extend several properties of <i>z</i>-ideals to <i>z</i>-elements and introduce various distinguished subclasses of <i>z</i>-elements, such as <i>z</i>-prime, <i>z</i>-semiprime, <i>z</i>-primary, <i>z</i>-irreducible, and <i>z</i>-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where <i>z</i>-elements are closed under finite products and a representation of <i>z</i>-elements in terms of <i>z</i>-irreducible elements in <i>z</i>-Noetherian multiplicative lattices.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":"86 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00012-024-00882-4.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra Universalis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00012-024-00882-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is to investigate further properties of z-elements in multiplicative lattices. We utilize z-closure operators to extend several properties of z-ideals to z-elements and introduce various distinguished subclasses of z-elements, such as z-prime, z-semiprime, z-primary, z-irreducible, and z-strongly irreducible elements, and study their properties. We provide a characterization of multiplicative lattices where z-elements are closed under finite products and a representation of z-elements in terms of z-irreducible elements in z-Noetherian multiplicative lattices.
期刊介绍：
Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.
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