{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T17:30:07Z","timestamp":1764783007622},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2007,5]]},"abstract":"<jats:p>We construct the inverse partition semigroup[Formula: see text], isomorphic to the dual symmetric inverse monoid[Formula: see text], introduced in [6]. We give a convenient geometric illustration for elements of [Formula: see text]. We describe all maximal subsemigroups of [Formula: see text] and find a generating set for [Formula: see text] when X is finite. We prove that all the automorphisms of [Formula: see text] are inner. We show how to embed the symmetric inverse semigroup into the inverse partition one. For finite sets X, we establish that, up to equivalence, there is a unique faithful effective transitive representation of [Formula: see text], namely to [Formula: see text]. Finally, we construct an interesting [Formula: see text]-cross-section of [Formula: see text], which is reminiscent of [Formula: see text], the [Formula: see text]-cross-section of [Formula: see text], constructed in [4].<\/jats:p>","DOI":"10.1142\/s0218196707003792","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T11:38:28Z","timestamp":1180525108000},"page":"567-591","source":"Crossref","is-referenced-by-count":13,"title":["ON A NEW APPROACH TO THE DUAL SYMMETRIC INVERSE MONOID $\\mathcal{I}_{X}^{\\ast}$"],"prefix":"10.1142","volume":"17","author":[{"given":"VICTOR","family":"MALTCEV","sequence":"first","affiliation":[{"name":"Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.2307\/1968843"},{"key":"rf3","first-page":"99","volume":"119","author":"Xi C.","journal-title":"Compos Math."},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196795000161"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700037692"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700039227"},{"key":"rf7","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198511946.001.0001","volume-title":"Fundamentals of Semigroup Theory","author":"Howie J. M.","year":"1995"},{"key":"rf8","first-page":"188","volume":"164","author":"Kerov S.","journal-title":"Zap. Nauchn. Sem. LOMI"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-005-0511-3"},{"key":"rf11","volume-title":"Group Theory","author":"Kurosh A. G.","year":"1967"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1080\/00927870600651414"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/3645"},{"key":"rf14","first-page":"59","volume":"2","author":"Maltcev V.","journal-title":"Rep. Kyiv Univ."},{"key":"rf15","first-page":"11","volume":"39","author":"Maltcev V.","journal-title":"Sci. Proc. Kyiv-Mohyla Acad."},{"key":"rf16","first-page":"101","volume":"16","author":"Maltcev V.","journal-title":"Rep. Kyiv Univ."},{"key":"rf18","first-page":"29","volume":"13","author":"Mazorchuk V.","journal-title":"Prob. Algebra"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120004500"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/BF02195904"},{"key":"rf21","volume-title":"Inverse Semigroups","author":"Petrich M.","year":"1984"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196707003792","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T16:45:01Z","timestamp":1707929101000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196707003792"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5]]},"references-count":18,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,5]]}},"alternative-id":["10.1142\/S0218196707003792"],"URL":"https:\/\/doi.org\/10.1142\/s0218196707003792","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,5]]}}}