Radical Theory for Group Semiautomata

  Y. Fong F.K. Huang R.Wiegandt

Abstract:

  A Kurosh-Amitsur radical theory is developed for group semiautomata. Radical theory stems from ring theory, it is apt for deriving structure theorems and for a comparative study of properties. Unlikely to conventional radical theories, the radical of a group semiautomaton need not be a subsemiautomaton, so the whole scene will take place in a suitably constructed category. The fundamental facts of the theory are described in 2. A special feature of the theory, the existence of complementary radicals, is discussed in 3. Restricting the theory to additive automata, which still comprise linear sequential machines, in 4 stronger results will be achieved, and also a (sub)direct decomposition theorem for certain semisimple group semiautomata will be proved. Examples are given at appropriate places. The paper may serve also as a framework for future structural investigations of group semiautomata.

  Keywords: Kurosh-Amitsur radical, group semiautomaton.

 Gyenizse Pal 1996. Szeptember 4. Szerda 13:18:14 MET DST