Abstract:
Motivated by several algorithmic problems related with computer sciences, researchers have devoted attention to the study of the theory of finite semigroups, particularly since late 70?s. Therefore, pseudovarieties (classes of finite semigroups closed under finite direct product, subsemigroup and homomorphic image) became objects of special consideration. The present dissertation is a small study of the join of two peudovarieties, one of the most important operators acting on pseudovarieties. The join of two pseudovarieties V V W is the smallest pseudovariety containing both V and W.
In this study, we will not, obviously, compute every join of pseudovariety known at the present. We will, instead, present some of the most usual thecniques for doing join computations.
At the end of this dissertation we will present a table to sumarize some of the known results on joins of pseudovarieties.