{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T19:39:15Z","timestamp":1694633955845},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,1,20]],"date-time":"2009-01-20T00:00:00Z","timestamp":1232409600000},"content-version":"unspecified","delay-in-days":5712,"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":[[1993,6]]},"abstract":"<jats:p>Some new concepts are introduced, in particular that of a unique factorization semilattice. Necessary and sufficient conditions are given for two principal ideals of the semilattice of idempotents of a free inverse monoid<jats:italic>FIM<\/jats:italic>(<jats:italic>X<\/jats:italic>) to be isomorphic and some properties of the Munn semigroup of<jats:italic>E<\/jats:italic>[<jats:italic>FIM<\/jats:italic>(<jats:italic>X<\/jats:italic>)] are obtained. Some results on the embedding of semilattices in<jats:italic>E<\/jats:italic>[<jats:italic>FIM<\/jats:italic>(<jats:italic>X<\/jats:italic>)] are also obtained.<\/jats:p>","DOI":"10.1017\/s0013091500018447","type":"journal-article","created":{"date-parts":[[2008,12,19]],"date-time":"2008-12-19T15:17:57Z","timestamp":1229699877000},"page":"349-360","source":"Crossref","is-referenced-by-count":1,"title":["On the semilattice of idempotents of a free inverse monoid"],"prefix":"10.1017","volume":"36","author":[{"given":"Pedro V.","family":"Silva","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,1,20]]},"reference":[{"key":"S0013091500018447_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1973-0310093-1"},{"key":"S0013091500018447_ref006","volume-title":"Inverse semigroups","author":"Petrich","year":"1984"},{"key":"S0013091500018447_ref004","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/21.2.157"},{"key":"S0013091500018447_ref003","volume-title":"Introduction to semigroup theory","author":"Howie","year":"1976"},{"key":"S0013091500018447_ref001","volume-title":"Groups, rings, modules","author":"Auslander","year":"1974"},{"key":"S0013091500018447_ref002","doi-asserted-by":"crossref","unstructured":"2. Clifford A. H. and Preston G. B. , The algebraic theory of semigroups (Math. Surveys 7, Providence, R.I., Amer. Math. Soc, 1961 (vol. 1) and 1967 (vol. II)).","DOI":"10.1090\/surv\/007.2\/02"},{"key":"S0013091500018447_ref007","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700045251"},{"key":"S0013091500018447_ref005","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-29.3.385"}],"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\/S0013091500018447","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T11:18:20Z","timestamp":1632827900000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0013091500018447\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,6]]},"references-count":8,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1993,6]]}},"alternative-id":["S0013091500018447"],"URL":"https:\/\/doi.org\/10.1017\/s0013091500018447","relation":{},"ISSN":["0013-0915","1464-3839"],"issn-type":[{"value":"0013-0915","type":"print"},{"value":"1464-3839","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,6]]}}}