{"title":"Low separation axioms in primal spaces and the Zariski Topology","authors":"Angel Guale, Jorge Vielma, Edgar Sanchez","doi":"10.1007/s13370-026-01507-w","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we give characterizations of the primal spaces that satisfy some separation axioms between <span>\\(T_0\\)</span> and <span>\\(T_1\\)</span> in terms of the function that generates the topology, and we establish which axioms are equivalent in this context. We also give a characterization of the rings whose prime spectrum, endowed with the Zariski topology, is a primal space.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"37 3","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-026-01507-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we give characterizations of the primal spaces that satisfy some separation axioms between \(T_0\) and \(T_1\) in terms of the function that generates the topology, and we establish which axioms are equivalent in this context. We also give a characterization of the rings whose prime spectrum, endowed with the Zariski topology, is a primal space.
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