SOLVING SYSTEMS OF EQUATIONS MODULO PSEUDOVARIETIES OF ABELIAN GROUPS AND HYPERDECIDABILITY

Abstract

Recall that a pseudovariety of monoids is a class of finite monoids closed under formation of finite direct products, submonoids and homomorphic images. Generalizing the notions of pointlike sets [11] and Type I and Type II semigroups [14, 15] Almeida [1] introduced the notion of hyperdecidability for pseudovarieties. One of the nice properties of a hyperdecidable pseudovariety W is that under relatively mild hypothesis on a pseudovariety V (decidable with finite vertex rank) one can decide membership in the semidirect product pseudovariety V ∗ W. Most proofs of hyperdecidability [4, 7, 16, 18] actually establish a somewhat stronger property called