{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T22:35:52Z","timestamp":1769553352931,"version":"3.49.0"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algebra Colloq."],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p> Let [Formula: see text] be the semigroup of all partial transformations on X, [Formula: see text] and [Formula: see text] be the subsemigroups of [Formula: see text] of all full transformations on X and of all injective partial transformations on X, respectively. Given a non-empty subset Y of X, let [Formula: see text], [Formula: see text] and [Formula: see text]. In 2008, Sanwong and Sommanee described the largest regular subsemigroup and determined Green's relations of [Formula: see text]. In this paper, we present analogous results for both [Formula: see text] and [Formula: see text]. For a finite set X with |X| \u2265 3, the ranks of [Formula: see text], [Formula: see text] and [Formula: see text] are well known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of [Formula: see text], [Formula: see text] and [Formula: see text] for any proper non-empty subset Y of X. <\/jats:p>","DOI":"10.1142\/s1005386714000431","type":"journal-article","created":{"date-parts":[[2014,6,24]],"date-time":"2014-06-24T08:05:31Z","timestamp":1403597131000},"page":"497-510","source":"Crossref","is-referenced-by-count":26,"title":["On the Ranks of Semigroups of Transformations on a Finite Set with Restricted Range"],"prefix":"10.1142","volume":"21","author":[{"given":"V\u00edtor H.","family":"Fernandes","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, Monte da Caparica, 2829-516 Caparica, Portugal"},{"name":"Centro de \u00c1lgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal"}]},{"given":"Jintana","family":"Sanwong","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"},{"name":"Material Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand"}]}],"member":"219","published-online":{"date-parts":[[2014,6,24]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500031553"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100066780"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500024355"},{"key":"p_5","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1017\/S0004972710001814","volume":"83","author":"Mendes-Gon\u00e7alves R.P","year":"2011","journal-title":"Bull. Austral. Math. Soc."},{"issue":"3","key":"p_6","first-page":"307","volume":"16","author":"Nenthein P.","year":"2005","journal-title":"Pure Math. Appl."},{"issue":"3","key":"p_7","first-page":"455","volume":"25","author":"Sanwong B.","year":"2009","journal-title":"Ser.)"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/794013"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1142\/S1005386707000259"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972708000385"},{"key":"p_11","first-page":"413","year":"1975","journal-title":"A) ("}],"container-title":["Algebra Colloquium"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1005386714000431","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T17:47:11Z","timestamp":1565200031000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1005386714000431"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,24]]},"references-count":10,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2014,6,24]]},"published-print":{"date-parts":[[2014,9]]}},"alternative-id":["10.1142\/S1005386714000431"],"URL":"https:\/\/doi.org\/10.1142\/s1005386714000431","relation":{},"ISSN":["1005-3867","0219-1733"],"issn-type":[{"value":"1005-3867","type":"print"},{"value":"0219-1733","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,24]]}}}