Monomial algebras

Belov, A.Y.; Borisenko, V.V.; Latyshev, V.N.

Авторы: Belov A.Ya, Borisenko V.V., Latyshev V.N.
Журнал: Journal of Mathematical Sciences
Том: 87
Номер: 3
Год издания: 1997
Издательство: Plenum Publishers
Местоположение издательства: United States
Первая страница: 3463
Последняя страница: 3575
DOI: 10.1007/BF02355446
Аннотация: The survey is devoted to study applications of combinatorial methods in ring theory. As the authors write in the Introduction, “we are more interested in the technique of obtaining these methods and not in the results themselves. … The main subject here is the word combinatorial analysis and its applications, and also the notion of the canonical form of elements in different calculi.” Monomial algebras, i.e., algebras whose defining relations are products of generators, are at the center of the survey. The authors study algorithmic problems in the theory of monomial algebras, the representations of such algebras, the varieties generated by them and their structure theory. A special attention is devoted to automata algebras, i.e., monomial algebras whose set of non-zero words is a regular language. The survey contains 8 chapters: 1. The word combinatorial theory and its applications; 2. Applications of the word analysis to problems of the Burnside type; 3. Uniformly recurrent words and radicals in monomial algebras; 4. The category of monomial algebras; 5. Automata algebras; 6. Representations of monomial algebras; 7. Varieties of monomial algebras; 8. Lie nilpotency: recognition and the word problem.Reviewer: B.Vernikov (Ekaterinburg)
Добавил в систему: Белов Алексей Яковлевич

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