{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T07:07:58Z","timestamp":1649142478062},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algebra Colloq."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p> We consider particular compatible orders on a given completely simple semigroup S<jats:sub>x<\/jats:sub>=M(\u3008x\u3009; I ,\u039b;P) where \u3008x\u3009 is an ordered cyclic group with x &gt; 1 and P<jats:sub>11<\/jats:sub>=x<jats:sup>-1<\/jats:sup>. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, S<jats:sub>x<\/jats:sub> is orthodox and has a biggest idempotent. With the bootlace order, the maximal idempotents of S<jats:sub>x<\/jats:sub> are identified by specific locations in the sandwich matrix. In the orthodox case there is also a biggest idempotent and, for sandwich matrices of a given size, uniqueness up to ordered semigroup isomorphism is established. <\/jats:p>","DOI":"10.1142\/s1005386714000145","type":"journal-article","created":{"date-parts":[[2014,4,11]],"date-time":"2014-04-11T04:16:29Z","timestamp":1397189789000},"page":"181-194","source":"Crossref","is-referenced-by-count":0,"title":["Residuated Completely Simple Semigroups"],"prefix":"10.1142","volume":"21","author":[{"given":"T. S.","family":"Blyth","sequence":"first","affiliation":[{"name":"Mathematical Institute, University of St Andrews, Scotland"}]},{"given":"G. A.","family":"Pinto","sequence":"additional","affiliation":[{"name":"Instituto Piaget, Campus Universit\u00e1rio de Almada, Quinta da Arreinela de Cima, 2800-305, Almada, Portugal"},{"name":"Universidade Atl\u00e2ntica, Instituto de Investiga\u00e7\u00e3o Cient\u00edfica e Tecnol\u00f3gica, F\u00e1brica da P\u00f3lvora, 2730-036, Barcarena, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2014,4,11]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(72)90112-3"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1080\/00927879308824651"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500009435"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500005770"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-100105033"},{"key":"p_7","first-page":"361","volume":"70","author":"Croisot R.","year":"1953","journal-title":"Norm. Sup."},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573443"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572827"}],"container-title":["Algebra Colloquium"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1005386714000145","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T08:23:31Z","timestamp":1565166211000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1005386714000145"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,11]]},"references-count":8,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2014,4,11]]},"published-print":{"date-parts":[[2014,6]]}},"alternative-id":["10.1142\/S1005386714000145"],"URL":"https:\/\/doi.org\/10.1142\/s1005386714000145","relation":{},"ISSN":["1005-3867","0219-1733"],"issn-type":[{"value":"1005-3867","type":"print"},{"value":"0219-1733","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4,11]]}}}