{"title":"半群构造的主权利理想的升链条件","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":"{\"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}","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}
The ascending chain condition on principal right ideals for semigroup constructions
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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