{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T07:50:07Z","timestamp":1648540207385},"reference-count":4,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,1,20]],"date-time":"2009-01-20T00:00:00Z","timestamp":1232409600000},"content-version":"unspecified","delay-in-days":5955,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Edinburgh Mathematical Society"],"published-print":{"date-parts":[[1992,10]]},"abstract":"<jats:p>We prove that in a residuated regular semigroup the elements of the form <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0013091500005770_inline1\" \/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" xlink:type=\"simple\" xlink:href=\"S0013091500005770_inline1\" \/> are idempotents, and derive some consequences of this fact. In particular, we show how the maximality of such idempotents is related to the semigroup being naturally ordered, and obtain from this a characterisation of the boot-lace semigroup of [2].<\/jats:p>","DOI":"10.1017\/s0013091500005770","type":"journal-article","created":{"date-parts":[[2008,12,19]],"date-time":"2008-12-19T10:41:00Z","timestamp":1229683260000},"page":"501-509","source":"Crossref","is-referenced-by-count":3,"title":["Residuated regular semigroups"],"prefix":"10.1017","volume":"35","author":[{"given":"T. S.","family":"Blyth","sequence":"first","affiliation":[]},{"given":"G. A.","family":"Pinto","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,1,20]]},"reference":[{"key":"S0013091500005770_ref004","doi-asserted-by":"publisher","DOI":"10.1017\/S001309150000688X"},{"key":"S0013091500005770_ref001","volume-title":"Residuation Theory","author":"Blyth","year":"1972"},{"key":"S0013091500005770_ref003","doi-asserted-by":"publisher","DOI":"10.1080\/00927879108824220"},{"key":"S0013091500005770_ref002","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500009435"}],"container-title":["Proceedings of the Edinburgh Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0013091500005770","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T16:33:18Z","timestamp":1558024398000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0013091500005770\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,10]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,10]]}},"alternative-id":["S0013091500005770"],"URL":"https:\/\/doi.org\/10.1017\/s0013091500005770","relation":{},"ISSN":["0013-0915","1464-3839"],"issn-type":[{"value":"0013-0915","type":"print"},{"value":"1464-3839","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,10]]}}}