{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:22:48Z","timestamp":1777422168921,"version":"3.51.4"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"crossref","award":["EP\/V002953\/1"],"award-info":[{"award-number":["EP\/V002953\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s0218196723500054","type":"journal-article","created":{"date-parts":[[2022,11,29]],"date-time":"2022-11-29T10:20:21Z","timestamp":1669717221000},"page":"47-66","source":"Crossref","is-referenced-by-count":1,"title":["The \u211b-height of semigroups and their bi-ideals"],"prefix":"10.1142","volume":"33","author":[{"given":"Craig","family":"Miller","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of York, York YO10 5DD, UK"}]}],"member":"219","published-online":{"date-parts":[[2022,11,28]]},"reference":[{"key":"S0218196723500054BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(84)90055-0"},{"key":"S0218196723500054BIB002","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-9771-7","volume-title":"String Rewriting Systems","author":"Book R.","year":"1993"},{"key":"S0218196723500054BIB003","doi-asserted-by":"crossref","first-page":"521","DOI":"10.2307\/2372195","volume":"70","author":"Clifford A.","year":"1948","journal-title":"Amer. J. Math."},{"key":"S0218196723500054BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196721400063"},{"key":"S0218196723500054BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-019-10039-8"},{"key":"S0218196723500054BIB007","volume-title":"Automata, Languages and Machines","author":"Eilenberg S.","year":"1976"},{"key":"S0218196723500054BIB008","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1007\/978-3-319-58747-9_12","volume-title":"CSR 2017: Computer Science \u2014 Theory and Applications","author":"Fleischer L.","year":"2017"},{"key":"S0218196723500054BIB009","first-page":"624","volume":"58","author":"Good R.","year":"1952","journal-title":"Bull. Amer. Math. Soc."},{"key":"S0218196723500054BIB010","volume-title":"An Introduction to Semigroup Theory","author":"Howie J.","year":"1995"},{"key":"S0218196723500054BIB011","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1145\/322217.322230","volume":"27","author":"Huet G.","year":"1980","journal-title":"J. ACM"},{"key":"S0218196723500054BIB012","first-page":"710","volume":"45","author":"Lajos S.","year":"1969","journal-title":"Proc. Japan Acad."},{"key":"S0218196723500054BIB013","doi-asserted-by":"crossref","first-page":"837","DOI":"10.2183\/pjab1945.47.SupplementI_837","volume":"47","author":"Lajos S.","year":"1971","journal-title":"Proc. Japan Acad."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196723500054","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T07:34:55Z","timestamp":1675668895000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196723500054"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,28]]},"references-count":12,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["10.1142\/S0218196723500054"],"URL":"https:\/\/doi.org\/10.1142\/s0218196723500054","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,28]]}}}