{"title":"The ℛ-height of semigroups and their bi-ideals","authors":"Craig Miller","doi":"10.1142/s0218196723500054","DOIUrl":null,"url":null,"abstract":"The [Formula: see text]-height of a semigroup [Formula: see text] is the height of the poset of [Formula: see text]-classes of [Formula: see text] Given a semigroup [Formula: see text] with finite [Formula: see text]-height, we establish bounds on the [Formula: see text]-height of bi-ideals, one-sided ideals and two-sided ideals; in particular, these substructures inherit the property of having finite [Formula: see text]-height. We then investigate whether these bounds can be attained.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":"s3-23 1","pages":"47-66"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Algebra Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218196723500054","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
The [Formula: see text]-height of a semigroup [Formula: see text] is the height of the poset of [Formula: see text]-classes of [Formula: see text] Given a semigroup [Formula: see text] with finite [Formula: see text]-height, we establish bounds on the [Formula: see text]-height of bi-ideals, one-sided ideals and two-sided ideals; in particular, these substructures inherit the property of having finite [Formula: see text]-height. We then investigate whether these bounds can be attained.
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