{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T22:53:48Z","timestamp":1680303228919},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"03n04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1999,6]]},"abstract":" This note introduces the notion of a hyperdecidable pseudovariety. This notion appears naturally in trying to prove decidability of the membership problem of semi-direct products of pseudovarieties of semigroups. It turns out to be a generalization of a notion introduced by C. J. Ash in connection with his proof of the \"type II\" theorem. <\/jats:p> The main results in this paper include a formulation of the definition of a hyper-decidable pseudovariety in terms of free profinite semigroups, the equivalence with Ash's property in the group case, the behaviour under the operator g of taking the associated global pseudovariety of semigroupoids, and the decidability of V*W in case gV is decidable and has a given finite vertex-rank and W is hyperdecidable. A further application of this notion which is given establishes that the join of a hyperdecidable pseudovariety with a locally finite pseudovariety with computable free objects is again hyperdecidable. <\/jats:p>","DOI":"10.1142\/s0218196799000163","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:05:54Z","timestamp":1027767954000},"page":"241-261","source":"Crossref","is-referenced-by-count":33,"title":["HYPERDECIDABLE PSEUDOVARIETIES AND THE CALCULATION OF SEMIDIRECT PRODUCTS"],"prefix":"10.1142","volume":"09","author":[{"given":"JORGE","family":"ALMEIDA","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica, Faculdade de Ci\u00eancias da Universidade do Porto, P. 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