Hyperdecidable Pseudovarieties and the Calculation of Semidirect Products (0)
| Venue: | Internat. J. Algebra Comput |
| Citations: | 15 - 6 self |
BibTeX
@ARTICLE{Almeida_hyperdecidablepseudovarieties,
author = {Jorge Almeida},
title = {Hyperdecidable Pseudovarieties and the Calculation of Semidirect Products},
journal = {Internat. J. Algebra Comput},
year = {},
volume = {9},
pages = {241--261}
}
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Abstract
This note introduces the notion of a hyperdecidable pseudovariety. This notion appears naturally in trying to prove decidability of the membership problem of semidirect 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. The main results in this paper include a formulation of the definition of a hyperdecidable 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. 1. Introduction A typical problem in...
