{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T16:19:47Z","timestamp":1648743587981},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,5,18]],"date-time":"2009-05-18T00:00:00Z","timestamp":1242604800000},"content-version":"unspecified","delay-in-days":6834,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Glasgow Math. J."],"published-print":{"date-parts":[[1990,9]]},"abstract":"<jats:p>An ordered semigroup <jats:italic>S<\/jats:italic> will be called <jats:italic>principally ordered<\/jats:italic> if, for every <jats:italic>x<\/jats:italic> \u025b <jats:italic>S<\/jats:italic>, there exists<\/jats:p><jats:p><jats:italic>x<jats:sup>*<\/jats:sup><\/jats:italic> = max {<jats:italic>y<\/jats:italic> \u025b <jats:italic>S<\/jats:italic>; <jats:italic>xyx<\/jats:italic> \u2264 <jats:italic>x<\/jats:italic>}.<\/jats:p><jats:p>Here we shall be concerned with the case where <jats:italic>S<\/jats:italic> is regular. We begin by listing some basic properties that arise from the above definition. As usual, we shall denote by <jats:italic>V<\/jats:italic>(<jats:italic>x<\/jats:italic>) the set of inverses of <jats:italic>x<\/jats:italic> \u025b <jats:italic>S<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0017089500009435","type":"journal-article","created":{"date-parts":[[2009,5,18]],"date-time":"2009-05-18T05:32:03Z","timestamp":1242624723000},"page":"349-364","source":"Crossref","is-referenced-by-count":11,"title":["Principally ordered regular semigroups"],"prefix":"10.1017","volume":"32","author":[{"given":"T. S.","family":"Blyth","sequence":"first","affiliation":[]},{"given":"G. A.","family":"Pinto","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,5,18]]},"reference":[{"key":"S0017089500009435_ref007","doi-asserted-by":"publisher","DOI":"10.1017\/S001309150000688X"},{"key":"S0017089500009435_ref006","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700019467"},{"key":"S0017089500009435_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700013756"},{"key":"S0017089500009435_ref003","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500012671"},{"key":"S0017089500009435_ref002","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500009859"},{"key":"S0017089500009435_ref001","volume-title":"Residuation Theory","author":"Blyth","year":"1972"},{"key":"S0017089500009435_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(83)90205-3"}],"container-title":["Glasgow Mathematical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0017089500009435","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T16:18:07Z","timestamp":1558196287000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0017089500009435\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1990,9]]}},"alternative-id":["S0017089500009435"],"URL":"https:\/\/doi.org\/10.1017\/s0017089500009435","relation":{},"ISSN":["0017-0895","1469-509X"],"issn-type":[{"value":"0017-0895","type":"print"},{"value":"1469-509X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,9]]}}}