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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Main Authors: | |
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Format: | Article |
Published: |
1994
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Series: | Acta cybernetica
11 No. 3 |
Kulcsszavak: | Számítástechnika, Kibernetika |
Subjects: | |
Online Access: | http://acta.bibl.u-szeged.hu/12527 |
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. |
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Physical Description: | 169-188 |
ISSN: | 0324-721X |