{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T19:40:10Z","timestamp":1708976410761},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2008,2,1]],"date-time":"2008-02-01T00:00:00Z","timestamp":1201824000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Aust. Math. Soc."],"published-print":{"date-parts":[[2008,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is known that, for semigroups, the property of admitting a finite presentation is preserved on passing to subsemigroups and extensions of finite Rees index. The present paper shows that the same holds true for Malcev, cancellative, left-cancellative and right-cancellative presentations. (A\u00a0Malcev (respectively, cancellative, left-cancellative, right-cancellative) presentation is a presentation of a special type that can be used to define any group-embeddable (respectively, cancellative, left-cancellative, right-cancellative) semigroup.)<\/jats:p>","DOI":"10.1017\/s1446788708000086","type":"journal-article","created":{"date-parts":[[2008,5,27]],"date-time":"2008-05-27T12:12:06Z","timestamp":1211890326000},"page":"39-61","source":"Crossref","is-referenced-by-count":4,"title":["CANCELLATIVE AND MALCEV PRESENTATIONS FOR FINITE REES INDEX SUBSEMIGROUPS AND EXTENSIONS"],"prefix":"10.1017","volume":"84","author":[{"given":"ALAN J.","family":"CAIN","sequence":"first","affiliation":[]},{"given":"EDMUND F.","family":"ROBERTSON","sequence":"additional","affiliation":[]},{"given":"NIK","family":"RU\u0160KUC","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2008,2,1]]},"reference":[{"key":"S1446788708000086_ref16","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198511946.001.0001","volume-title":"Fundamentals of semigroup theory","author":"Howie","year":"1995"},{"key":"S1446788708000086_ref14","doi-asserted-by":"crossref","DOI":"10.1201\/9781439865699","volume-title":"Word processing in groups","author":"Epstein","year":"1992"},{"key":"S1446788708000086_ref13","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1449"},{"key":"S1446788708000086_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004106009236"},{"key":"S1446788708000086_ref8","doi-asserted-by":"publisher","DOI":"10.1515\/JGT.2006.027"},{"key":"S1446788708000086_ref6","unstructured":"[6] Cain A.\u00a0J. , \u2018Automatism of subsemigroups of Baumslag\u2013Solitar semigroups\u2019, submitted."},{"key":"S1446788708000086_ref5","doi-asserted-by":"crossref","unstructured":"[5] Cain A.\u00a0J. , \u2018Malcev presentations for subsemigroups of direct products of coherent groups\u2019, J. Pure Appl. Algebra, to appear.","DOI":"10.1016\/j.jpaa.2008.10.006"},{"key":"S1446788708000086_ref2","article-title":"Defining relations and algorithmic problems for groups and semigroups","volume":"85","author":"Adjan","year":"1966","journal-title":"P. Steklov Inst. Math."},{"key":"S1446788708000086_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02573619"},{"key":"S1446788708000086_ref3","unstructured":"[3] Ara\u00fajo I.\u00a0M. , Silva P.\u00a0V. and Ru\u0161kuc N. , \u2018Presentations for inverse subsemigroups with finite complement\u2019, submitted."},{"key":"S1446788708000086_ref21","doi-asserted-by":"publisher","DOI":"10.1112\/S0024611598000124"},{"key":"S1446788708000086_ref1","article-title":"Defining relations and algorithmic problems for groups and semigroups","volume":"85","author":"Adjan","year":"1966","journal-title":"Tr. Mat. Inst. Steklova"},{"key":"S1446788708000086_ref11","volume-title":"The algebraic theory of semigroups","volume":"Vol.\u00a0I","author":"Clifford","year":"1961"},{"key":"S1446788708000086_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511721212.018"},{"key":"S1446788708000086_ref20","unstructured":"[20] Ru\u0161kuc N. , \u2018Semigroup presentations\u2019, PhD Thesis, University of St Andrews, 1995. http:\/\/turnbull.mcs.st-and.ac.uk\/\u223cnik\/Papers\/thesis.ps."},{"key":"S1446788708000086_ref17","first-page":"813","article-title":"Determining ideals of a given finite index in a finitely presented semigroup","volume":"11","author":"Jura","year":"1978","journal-title":"Demonstratio Math."},{"key":"S1446788708000086_ref15","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198535775.001.0001","volume-title":"Techniques of semigroup theory","author":"Higgins","year":"1992"},{"key":"S1446788708000086_ref22","doi-asserted-by":"publisher","DOI":"10.1007\/BF02194675"},{"key":"S1446788708000086_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(89)90043-1"},{"key":"S1446788708000086_ref4","unstructured":"[4] Cain A.\u00a0J. , \u2018Presentations for subsemigroups of groups\u2019, PhD Thesis, University of St\u00a0Andrews, 2005. http:\/\/www-groups.mcs.st-and.ac.uk\/\u223calanc\/publications\/c_phdthesis\/c_phdthesis.pdf."},{"key":"S1446788708000086_ref12","volume-title":"The algebraic theory of semigroups","volume":"Vol.\u00a0II","author":"Clifford","year":"1967"},{"key":"S1446788708000086_ref19","first-page":"331","article-title":"On the immersion of associative systems in groups","volume":"6","author":"Malcev","year":"1939","journal-title":"Mat. 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