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TitleRecognition of certain properties of automaton algebras.
Author(s) S.A. Ilyasov
TypeArticle in Journal
AbstractThe paper considers a new algebraic object, the completely automaton binomial algebras, which generalize certain existing classes of algebras. The author presents a classification of semigroup algebras taking into account completely automaton algebras and gives the corresponding examples. A number of standard algorithmic problems are solved for completely automaton binomial algebras: the recognition of a strict and nonstrict polynomial property, the recognition of the right and/or left finite processing, and the construction of the determining regular language for an algebra with finite processing and for monomial subalgebras of a free associative algebra and certain completely automaton algebras. For an automaton monomial algebra, the author constructs the left syzygy module of a finite system of elements and the Gröbner basis of a finitely generated left ideal; also, some algorithmic problems are solved.
ISSN1072-3374; 1573-8795/e
URL http://link.springer.com/article/10.1007%2Fs10958-008-9048-9
JournalJ. Math. Sci., New York
PublisherSpringer US, New York, NY
Translation No
Refereed No