{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T03:18:43Z","timestamp":1648783123351},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2009,1,20]],"date-time":"2009-01-20T00:00:00Z","timestamp":1232409600000},"content-version":"unspecified","delay-in-days":6443,"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":[[1991,6]]},"abstract":"<jats:p>Implicit operations (new operations commuting with all old homomorphisms) on pseudovarieties have been shown to play an important role in the study of these classes. They may be used to axiomatize sub-pseudovariaties and to describe recognizable subsets of (relatively) free objects. This paper presents a case study for the pseudovariety <jats:italic>CS<\/jats:italic> consisting of all finite simple semigroups. Based on a result of profinite group theory, a structural description of semigroups of implicit operations on finite simple semigroups is used to deduce that <jats:italic>CS<\/jats:italic> is join-irreducible.<\/jats:p>","DOI":"10.1017\/s0013091500007112","type":"journal-article","created":{"date-parts":[[2008,12,19]],"date-time":"2008-12-19T10:19:20Z","timestamp":1229681960000},"page":"205-215","source":"Crossref","is-referenced-by-count":2,"title":["On finite simple semigroups"],"prefix":"10.1017","volume":"34","author":[{"given":"Jorge","family":"Almeida","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,1,20]]},"reference":[{"key":"S0013091500007112_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(85)90147-4"},{"key":"S0013091500007112_ref019","unstructured":"19. Pin J.-E. , Topologies for the free monoid (LITP report 88\u201317), (to appear in J. Algebra)."},{"key":"S0013091500007112_ref003","first-page":"313","article-title":"Residually finite congruences and quasi-regular subsets in uniform algebras","volume":"46","author":"Almeida","year":"1989","journal-title":"Portugal. Math."},{"key":"S0013091500007112_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190713"},{"key":"S0013091500007112_ref010","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(79)90139-X"},{"key":"S0013091500007112_ref018","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-2215-3"},{"key":"S0013091500007112_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01243870"},{"key":"S0013091500007112_ref017","volume-title":"Semigroups and Combinatorial Applications","author":"Lallement","year":"1979"},{"key":"S0013091500007112_ref006","doi-asserted-by":"crossref","unstructured":"6. Almeida J. and Azevedo A. , Implicit operations on certain classes of semigroups, in S. Goberstein and P. Higgins (Eds.), Semigroups and their Applications (Proceedings 1986 Chico Conf., D. Reidel, 1987), 1\u201311.","DOI":"10.1007\/978-94-009-3839-7_1"},{"key":"S0013091500007112_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(76)90029-3"},{"key":"S0013091500007112_ref005","unstructured":"5. 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