{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T01:46:36Z","timestamp":1775526396786,"version":"3.50.1"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"1-2","license":[{"start":{"date-parts":[[2011,11,14]],"date-time":"2011-11-14T00:00:00Z","timestamp":1321228800000},"content-version":"unspecified","delay-in-days":10544,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"published-print":{"date-parts":[[1983]]},"abstract":"<jats:title>Synopsis<\/jats:title><jats:p>The existence of a smallest inverse congruence on an orthodox semigroup is known. It is also known that a regular semigroup<jats:italic>S<\/jats:italic>is locally inverse and orthodox if and only if there exists a local isomorphism from<jats:italic>S<\/jats:italic>onto an inverse semigroup<jats:italic>T<\/jats:italic>.<\/jats:p><jats:p>In this paper, we show the existence of a smallest<jats:italic>R<\/jats:italic>-unipotent congruence \u03c1 on an orthodox semigroup<jats:italic>S<\/jats:italic>and give its expression in the case where<jats:italic>S<\/jats:italic>is also left quasinormal. Finally, we prove that a regular semigroup<jats:italic>S<\/jats:italic>is left quasinormal and orthodox if and only if there exists a local isomorphism from<jats:italic>S<\/jats:italic>onto an<jats:italic>R<\/jats:italic>-unipotent semigroup<jats:italic>T<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0308210500015791","type":"journal-article","created":{"date-parts":[[2011,11,14]],"date-time":"2011-11-14T13:13:13Z","timestamp":1321276393000},"page":"59-71","source":"Crossref","is-referenced-by-count":5,"title":["On left quasinormal orthodox semigroups"],"prefix":"10.1017","volume":"95","author":[{"given":"Gracinda M. S.","family":"Gomes","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2011,11,14]]},"reference":[{"key":"S0308210500015791_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574170"},{"key":"S0308210500015791_ref012","first-page":"197","article-title":"Coextensions of regular semigroups by rectangular bands I","volume":"269","author":"Meakin","year":"1982","journal-title":"Trans. Amer. Math. Soc."},{"key":"S0308210500015791_ref009","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700009794"},{"key":"S0308210500015791_ref008","unstructured":"8 McAlister D. B. . Rees matrix covers for locally inverse semigroups, (to appear)."},{"key":"S0308210500015791_ref017","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1967.21.371"},{"key":"S0308210500015791_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500016140"},{"key":"S0308210500015791_ref007","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700019467"},{"key":"S0308210500015791_ref018","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1970.33.261"},{"key":"S0308210500015791_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02194660"},{"key":"S0308210500015791_ref004","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700041447"},{"key":"S0308210500015791_ref005","volume-title":"An introduction to Semigroup Theory","author":"Howie","year":"1976"},{"key":"S0308210500015791_ref006","doi-asserted-by":"publisher","DOI":"10.1017\/S2040618500035334"},{"key":"S0308210500015791_ref010","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700013665"},{"key":"S0308210500015791_ref011","unstructured":"11 Meakin J. C. . The Rees construction in regular semigroups. (Submitted)."},{"key":"S0308210500015791_ref013","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500003801"},{"key":"S0308210500015791_ref014","doi-asserted-by":"crossref","DOI":"10.1515\/9783112471326","volume-title":"Lectures in Semigroups","author":"Petrich","year":"1977"},{"key":"S0308210500015791_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(74)90064-7"},{"key":"S0308210500015791_ref016","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1976.63.555"}],"container-title":["Proceedings of the Royal Society of Edinburgh: Section A Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0308210500015791","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,11]],"date-time":"2023-06-11T03:36:12Z","timestamp":1686454572000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0308210500015791\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983]]},"references-count":18,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[1983]]}},"alternative-id":["S0308210500015791"],"URL":"https:\/\/doi.org\/10.1017\/s0308210500015791","relation":{},"ISSN":["0308-2105","1473-7124"],"issn-type":[{"value":"0308-2105","type":"print"},{"value":"1473-7124","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983]]}}}