{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:16:18Z","timestamp":1758280578717},"reference-count":8,"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":5738,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Glasgow Math. J."],"published-print":{"date-parts":[[1993,9]]},"abstract":"<jats:p>The relation \u211b* is defined on a semigroup <jats:italic>S<\/jats:italic> by the rule that \u211b*<jats:italic>b<\/jats:italic> if and only if the elements <jats:italic>a, b<\/jats:italic> of <jats:italic>S<\/jats:italic> are related by the Green's relation \u211b in some oversemigroup of <jats:italic>S<\/jats:italic>. A semigroup <jats:italic>S<\/jats:italic> is an <jats:italic>E<\/jats:italic>-semigroup if its set <jats:italic>E(S)<\/jats:italic>of idempotents is a subsemilattice of <jats:italic>S<\/jats:italic>. A left adequate semigroup is an <jats:italic>E<\/jats:italic>-semigroup in which every \u211b*-class contains an idempotent. It is easy to see that, in fact, each \u211b*-class of a left adequate semigroup contains a unique idempotent [2]. We denote the idempotent in the \u211b*-class of <jats:italic>a<\/jats:italic> by <jats:italic>a<\/jats:italic><jats:sup>+<\/jats:sup>.<\/jats:p>","DOI":"10.1017\/s0017089500009873","type":"journal-article","created":{"date-parts":[[2009,5,18]],"date-time":"2009-05-18T05:27:39Z","timestamp":1242624459000},"page":"293-306","source":"Crossref","is-referenced-by-count":16,"title":["Proper left type-<i>A<\/i> monoids revisited"],"prefix":"10.1017","volume":"35","author":[{"given":"John","family":"Fountain","sequence":"first","affiliation":[]},{"given":"Gracinda M. S.","family":"Gomes","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,5,18]]},"reference":[{"key":"S0017089500009873_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-74-99950-4"},{"key":"S0017089500009873_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(76)90023-5"},{"key":"S0017089500009873_ref001","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/28.3.285"},{"key":"S0017089500009873_ref002","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500016230"},{"key":"S0017089500009873_ref006","first-page":"227","article-title":"Groups, semilattices and inverse semigroups","volume":"192","author":"McAlister","year":"1974","journal-title":"Trans. Amer. Math. Soc."},{"key":"S0017089500009873_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(92)90066-O"},{"key":"S0017089500009873_ref004","first-page":"85","volume-title":"Proc. 1984 Marquette Conf. on Semigroups","author":"Margolis","year":"1985"},{"key":"S0017089500009873_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(87)90046-9"}],"container-title":["Glasgow Mathematical Journal"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0017089500009873","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T17:48:43Z","timestamp":1557942523000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0017089500009873\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,9]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,9]]}},"alternative-id":["S0017089500009873"],"URL":"https:\/\/doi.org\/10.1017\/s0017089500009873","relation":{},"ISSN":["0017-0895","1469-509X"],"issn-type":[{"value":"0017-0895","type":"print"},{"value":"1469-509X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,9]]}}}