Torsion theory on semigroup automata

In this report we study the torsion theory on the semigroup automata. Our main tools are the right congruences on either the semigroup or the automata.;Let S be a fixed semigroup. We first start by working on a specific type of torsion, namely, the A-torsion associated with the right denominator set A of S and use it to characterize certain automata of fractions. This turns out to be the principal example and motivation for our general torsion concept.;In the second chapter we define the hereditary pretorsion class of S-automata as a set of S-automata which is closed under subautomata, quotients, coproducts and finite direct products. We are able to establish the bijective correspondence between the hereditary pretorsion classes of S-automata, the right linear topologies on S with an identity adjoined and the idempotent preradicals r on the category of S-automata such that the set Cr = ;Finally, we define the hereditary torsion class of S-automata to be the hereditary pretorsion class which is also closed under extensions. We then extend the previous correspondence to a bijective correspondence between the hereditary torsion classes, the right Gabriel topologies and the idempotent radicals such that the above condition holds.