{"title":"The ascending chain condition on principal right ideals for semigroup constructions","authors":"Craig Miller","doi":"10.1007/s10998-023-00570-1","DOIUrl":null,"url":null,"abstract":"<p>We call a semigroup <span>\\({\\mathcal {R}}\\)</span><i>-noetherian</i> if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on <span>\\({\\mathcal {R}}\\)</span>-classes. We investigate the behaviour of the property of being <span>\\({\\mathcal {R}}\\text {-noetherian}\\)</span> under the following standard semigroup-theoretic constructions: semidirect products, Schützenberger products, free products, Rees matrix semigroups, Brandt extensions, Bruck–Reilly extensions and semilattices of semigroups.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10998-023-00570-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We call a semigroup \({\mathcal {R}}\)-noetherian if it satisfies the ascending chain condition on principal right ideals, or, equivalently, the ascending chain condition on \({\mathcal {R}}\)-classes. We investigate the behaviour of the property of being \({\mathcal {R}}\text {-noetherian}\) under the following standard semigroup-theoretic constructions: semidirect products, Schützenberger products, free products, Rees matrix semigroups, Brandt extensions, Bruck–Reilly extensions and semilattices of semigroups.
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