{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T16:05:52Z","timestamp":1648656352124},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,11]]},"abstract":"<jats:p> A semigroup of languages is a set of languages considered with (and closed under) the operation of catenation. In other words, semigroups of languages are subsemigroups of power-semigroups of free semigroups. We prove that a (finite) semigroup is positively ordered if and only if it is a homomorphic image, under an order-preserving homomorphism, of a (finite) semigroup of languages. Hence it follows that a finite semigroup is [Formula: see text]-trivial if and only if it is a homomorphic image of a finite semigroup of languages. <\/jats:p>","DOI":"10.1142\/s021819670800486x","type":"journal-article","created":{"date-parts":[[2008,11,27]],"date-time":"2008-11-27T08:36:08Z","timestamp":1227774968000},"page":"1223-1229","source":"Crossref","is-referenced-by-count":3,"title":["ORDERED AND $\\mathcal{J}$-TRIVIAL SEMIGROUPS AS DIVISORS OF SEMIGROUPS OF LANGUAGES"],"prefix":"10.1142","volume":"18","author":[{"given":"ALEXEI","family":"VERNITSKI","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Essex, Colchester, Essex, C04 3SQ, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"Finite Semigroups and Universal Algebra","author":"Almeida J.","year":"1994"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196705002116"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(00)00434-5"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(96)00230-7"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573319"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-2215-3"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(97)00037-X"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1080\/00207169808804692"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572507"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90067-1"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196704002018"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819670800486X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:20:14Z","timestamp":1565115614000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819670800486X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,11]]},"references-count":11,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,11]]}},"alternative-id":["10.1142\/S021819670800486X"],"URL":"https:\/\/doi.org\/10.1142\/s021819670800486x","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,11]]}}}