{"title":"Commutant properties of w-core inverses","authors":"Chengcheng Wang , Huihui Zhu , Julio Benítez","doi":"10.1016/j.kjs.2025.100390","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate commutant properties of the <span><math><mi>w</mi></math></span>-core inverse in a <span><math><mo>∗</mo></math></span>-semigroup. Among these, it is shown that <figure><img></figure> if and only if <span><math><mi>a</mi></math></span> is equal projection (EP) with <figure><img></figure> , where <span><math><mi>a</mi></math></span> and <span><math><mi>w</mi></math></span> are elements of a <span><math><mo>∗</mo></math></span>-semigroup. As applications, equivalent conditions such that a core invertible element is an EP element are given. Then, commutant properties of the <span><math><mi>w</mi></math></span>-core inverse for complex matrices are correspondingly given. Finally, some results on double commutants and the reverse order law for <span><math><mi>w</mi></math></span>-core inverses are given.</div></div>","PeriodicalId":17848,"journal":{"name":"Kuwait Journal of Science","volume":"52 2","pages":"Article 100390"},"PeriodicalIF":1.2000,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kuwait Journal of Science","FirstCategoryId":"103","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2307410825000343","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
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Abstract
In this paper, we investigate commutant properties of the -core inverse in a -semigroup. Among these, it is shown that if and only if is equal projection (EP) with , where and are elements of a -semigroup. As applications, equivalent conditions such that a core invertible element is an EP element are given. Then, commutant properties of the -core inverse for complex matrices are correspondingly given. Finally, some results on double commutants and the reverse order law for -core inverses are given.
期刊介绍：
Kuwait Journal of Science (KJS) is indexed and abstracted by major publishing houses such as Chemical Abstract, Science Citation Index, Current contents, Mathematics Abstract, Micribiological Abstracts etc. KJS publishes peer-review articles in various fields of Science including Mathematics, Computer Science, Physics, Statistics, Biology, Chemistry and Earth & Environmental Sciences. In addition, it also aims to bring the results of scientific research carried out under a variety of intellectual traditions and organizations to the attention of specialized scholarly readership. As such, the publisher expects the submission of original manuscripts which contain analysis and solutions about important theoretical, empirical and normative issues.
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