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Recognition of certain properties of automaton algebras

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Abstract. The 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.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    S. A. Ilyasov

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  1. S. A. Ilyasov
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 20, Algebra, 2006.

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Ilyasov, S.A. Recognition of certain properties of automaton algebras. J Math Sci 152, 95–136 (2008). https://doi.org/10.1007/s10958-008-9048-9

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  • DOI: https://doi.org/10.1007/s10958-008-9048-9

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