Geodesic
Recognition of Certain Properties of Automaton Algebras
Contemporary Mathematics. Fundamental Directions, Algebra, Tome 20 (2006), pp. 104-147

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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 non-strict 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. 
@article{CMFD_2006_20_a2,
     author = {S. A. Ilyasov},
     title = {Recognition of {Certain} {Properties} of {Automaton} {Algebras}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {104--147},
     publisher = {mathdoc},
     volume = {20},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2006_20_a2/}
}
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S. A. Ilyasov. Recognition of Certain Properties of Automaton Algebras. Contemporary Mathematics. Fundamental Directions, Algebra, Tome 20 (2006), pp. 104-147. http://geodesic.mathdoc.fr/item/CMFD_2006_20_a2/