{"title":"Note on cyclic doppelsemigroups","authors":"V. Gavrylkiv","doi":"10.12958/adm1991","DOIUrl":null,"url":null,"abstract":"A doppelsemigroup (G,⊣,⊢) is calledcyclic if (G,⊣) is a cyclic group. In the paper, we describe up to isomorphism all cyclic (strong) doppelsemigroups. We prove that up to isomorphism there exist τ(n) finite cyclic (strong) doppelsemigroups of order n, where τ is the number of divisors function. Also there exist infinite countably many pairwise non-isomorphic infinite cyclic (strong) doppelsemigroups.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra & Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm1991","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 2
Abstract
A doppelsemigroup (G,⊣,⊢) is calledcyclic if (G,⊣) is a cyclic group. In the paper, we describe up to isomorphism all cyclic (strong) doppelsemigroups. We prove that up to isomorphism there exist τ(n) finite cyclic (strong) doppelsemigroups of order n, where τ is the number of divisors function. Also there exist infinite countably many pairwise non-isomorphic infinite cyclic (strong) doppelsemigroups.
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