Radical theory for group semiautomata

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 subsemiautoma...

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Bibliographic Details
Main Authors: Fong Yuen
Huang Feng-Kuo
Wiegandt Richard
Format: Article
Published: 1994
Series:Acta cybernetica 11 No. 3
Kulcsszavak:Számítástechnika, Kibernetika
Subjects:
Online Access:http://acta.bibl.u-szeged.hu/12527
Description
Summary: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.
Physical Description:169-188
ISSN:0324-721X