## Hyperdecidable Pseudovarieties and the Calculation of Semidirect Products (0)

Venue: | Internat. J. Algebra Comput |

Citations: | 16 - 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}

}

### Years of Citing Articles

### OpenURL

### 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...