{"title":"The maximal subsemigroups of the ideals in a monoid of partial injections","authors":"Apatsara Sareeto, Jörg Koppitz","doi":"10.1007/s00233-024-10439-5","DOIUrl":null,"url":null,"abstract":"<p>We study a submonoid of the well studied monoid <span>\\(POI_n\\)</span> of all order-preserving partial injections on an <i>n</i>-element chain. The set <span>\\(IOF_n^{par}\\)</span> of all partial transformations in <span>\\(POI_n\\)</span> which are fence-preserving as well as parity-preserving forms a submonoid of <span>\\(POI_n\\)</span>. We describe Green’s relations and ideals of <span>\\(IOF_n^{par}\\)</span>. For each ideal of <span>\\(IOF_n^{par}\\)</span>, we characterize the maximal subsemigroups. We observe that there are three different types of maximal subsemigroups.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","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/s00233-024-10439-5","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 study a submonoid of the well studied monoid \(POI_n\) of all order-preserving partial injections on an n-element chain. The set \(IOF_n^{par}\) of all partial transformations in \(POI_n\) which are fence-preserving as well as parity-preserving forms a submonoid of \(POI_n\). We describe Green’s relations and ideals of \(IOF_n^{par}\). For each ideal of \(IOF_n^{par}\), we characterize the maximal subsemigroups. We observe that there are three different types of maximal subsemigroups.
分享
京公网安备 11010802042870号
京ICP备2023020795号-1
求助内容：
应助结果提醒方式：
扫码关注我们
