On the hyperdecidability of semidirect products of pseudovarieties

Abstract

The notion of hyperdecidability has been introduced as a tool which is particularly suited for granting decidability of semidirect products. It is shown in this paper that the semidirect product of an hyperdecidable pseudovariety with a pseudovariety whose finitely generated free objects are finite and effectively computable is again hyperdecidable. As instances of this result, one obtains, for example, the hyperdecidability of the pseudovarieties of ail finite completely simple semigroups and of all finite bands of left groups.

^*This work was supported, in part, by P.C.T. and the project Praxis XXI/2/2.1/MAT/83/94

^*This work was supported, in part, by P.C.T. and the project Praxis XXI/2/2.1/MAT/83/94

Notes

^*This work was supported, in part, by P.C.T. and the project Praxis XXI/2/2.1/MAT/83/94