{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T18:40:36Z","timestamp":1649184036884},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,1,20]],"date-time":"2009-01-20T00:00:00Z","timestamp":1232409600000},"content-version":"unspecified","delay-in-days":5467,"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":[[1994,2]]},"abstract":"<jats:p>We show that an inverse transversal of a regular semigroup is multiplicative if and only if it is both weakly multiplicative and a quasi-ideal. Examples of quasi-ideal inverse transversals that are not multiplicative are known. Here we give an example of a weakly multiplicative inverse transversal that is not multiplicative. An interesting feature of this example is that it also serves to show that, in an ordered regular semigroup in which every element <jats:italic>x<\/jats:italic> has a biggest inverse <jats:italic>x<\/jats:italic><jats:sup>0<\/jats:sup>, the mapping <jats:italic>x<\/jats:italic>\u21a6<jats:italic>x<\/jats:italic><jats:sup>00<\/jats:sup> is not in general a closure; nor is <jats:italic>x<\/jats:italic>\u21a6<jats:italic>x<\/jats:italic>** in a principally ordered regular semigroup.<\/jats:p>","DOI":"10.1017\/s001309150001871x","type":"journal-article","created":{"date-parts":[[2008,12,19]],"date-time":"2008-12-19T15:38:59Z","timestamp":1229701139000},"page":"91-99","source":"Crossref","is-referenced-by-count":8,"title":["On weakly multiplicative inverse transversals"],"prefix":"10.1017","volume":"37","author":[{"given":"T. S.","family":"Blyth","sequence":"first","affiliation":[]},{"given":"M. H. Almeida","family":"Santos","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,1,20]]},"reference":[{"key":"S001309150001871X_ref014","unstructured":"14. Tang Xilin , Regular semigroups with inverse transversals (preprint)."},{"key":"S001309150001871X_ref006","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/35.4.455"},{"key":"S001309150001871X_ref002","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500009435"},{"key":"S001309150001871X_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573188"},{"key":"S001309150001871X_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572789"},{"key":"S001309150001871X_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572659"},{"key":"S001309150001871X_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573196"},{"key":"S001309150001871X_ref013","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500006891"},{"key":"S001309150001871X_ref012","doi-asserted-by":"publisher","DOI":"10.1017\/S001309150000688X"},{"key":"S001309150001871X_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1952-0050559-1"},{"key":"S001309150001871X_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500032522"},{"key":"S001309150001871X_ref008","first-page":"22","volume-title":"Proc. 8th Symposium on Semigroups","author":"Saito","year":"1985"},{"key":"S001309150001871X_ref007","first-page":"1","article-title":"Rectangular bands of inverse semigroups","volume":"56","author":"Pastijn","year":"1982","journal-title":"Simon Stevin"},{"key":"S001309150001871X_ref005","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/34.4.459"}],"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\/S001309150001871X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T19:22:34Z","timestamp":1557948154000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S001309150001871X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,2]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1994,2]]}},"alternative-id":["S001309150001871X"],"URL":"https:\/\/doi.org\/10.1017\/s001309150001871x","relation":{},"ISSN":["0013-0915","1464-3839"],"issn-type":[{"value":"0013-0915","type":"print"},{"value":"1464-3839","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,2]]}}}