F. Al-Kharousi, G. U. Garba, M. J. Ibrahim, A. T. Imam, A. Umar
{"title":"On the semigroup of finite order-preserving partial injective contraction mappings","authors":"F. Al-Kharousi, G. U. Garba, M. J. Ibrahim, A. T. Imam, A. Umar","doi":"10.1007/s13370-025-01259-z","DOIUrl":null,"url":null,"abstract":"<div><p>We initiate the algebraic study of the semigroup of one-to-one order-preserving partial contraction mappings of a totally ordered set <span>\\(\\{1,2,\\ldots ,n\\}\\)</span>, which we denote by <span>\\(\\mathcal {OCI}_{n}\\)</span>. In particular, we characterise the Green’s relations and their starred analogues in <span>\\(\\mathcal {OCI}_{n}\\)</span>. We also compute the rank of <span>\\(\\mathcal {OCI}_{n}\\)</span> as <span>\\(2n-1\\)</span>.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2025-02-04","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/s13370-025-01259-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We initiate the algebraic study of the semigroup of one-to-one order-preserving partial contraction mappings of a totally ordered set \(\{1,2,\ldots ,n\}\), which we denote by \(\mathcal {OCI}_{n}\). In particular, we characterise the Green’s relations and their starred analogues in \(\mathcal {OCI}_{n}\). We also compute the rank of \(\mathcal {OCI}_{n}\) as \(2n-1\).
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