Details:
Title  Recognition of certain properties of automaton algebras.  Author(s)  S.A. Ilyasov  Type  Article in Journal  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.  ISSN  10723374; 15738795/e 
URL 
http://link.springer.com/article/10.1007%2Fs1095800890489 
Language  English  Journal  J. Math. Sci., New York  Volume  152  Number  1  Pages  95136  Publisher  Springer US, New York, NY  Year  2008  Edition  0  Translation 
No  Refereed 
No 
