J2 Radical in Automata Nearrings

Abstract

Looking at the automata defined over a group alphabet as a nearring, we see that they are a highly complicated structure. As with ring theory, one method to deal with complexity is to look at semisimplicity modulo radical structures. We find some bounds on the Jacobson 2-radical and show that in certain groups, this radical can be explicitly found and the semisimple image determined.