Reiterman‘s theorem for pseudovarieties

Abstract

In this thesis we will restrict our attention only to classes of finite algebras. Besides the inherent motivation in studying finite algebras, they appear and are used in many other fields. For example, finite semigroups and monoids are very useful in the theory of au tomata and rational languages (see [22] and [9]). In particular, the classes considered in this context have some special properties, namely, they are closed under homomorphic images, under subsemigoups and under finite products. This motivates the general definition of a pseudovariety, which is a class of finite algebras closed under homomorphic images, under subalgebras and under finite products.