{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:35Z","timestamp":1761611195101},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:p>We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable.<\/jats:p>","DOI":"10.1142\/s0218196706003426","type":"journal-article","created":{"date-parts":[[2006,12,29]],"date-time":"2006-12-29T11:20:11Z","timestamp":1167391211000},"page":"1131-1159","source":"Crossref","is-referenced-by-count":9,"title":["IDENTITIES IN THE ALGEBRA OF PARTIAL MAPS"],"prefix":"10.1142","volume":"16","author":[{"given":"MARCEL","family":"JACKSON","sequence":"first","affiliation":[{"name":"Department of Mathematics, La Trobe University, Victoria 3086, Australia"}]},{"given":"TIM","family":"STOKES","sequence":"additional","affiliation":[{"name":"Mathematics, University of Waikato, Hamilton, New Zealand"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572784"},{"key":"rf3","doi-asserted-by":"crossref","unstructured":"B.\u00a0Buchberger and R.\u00a0Loos, Computer Algebra. Symbolic and Algebraic Computation, eds. B.\u00a0Buchberger, B. G.\u00a0Collins and R.\u00a0Loos (Springer-Verlag, New York, 1983)\u00a0pp. 11\u201343.","DOI":"10.1007\/978-3-7091-7551-4_2"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120016022"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500008168"},{"key":"rf6","unstructured":"V. S.\u00a0Garvac'ki\u012d, Theory of Semigroups and its Applications, No. 2 (Izdat. Saratov. Uni., Saratov, 1971)\u00a0pp. 2\u201313."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196799000412"},{"key":"rf8","first-page":"247","volume":"24","author":"Higman G.","journal-title":"J. London Math. Soc."},{"key":"rf9","series-title":"London Mathematical Society Monographs","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198511946.001.0001","volume-title":"Fundamentals of Semigroup Theory","author":"Howie J. 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