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Canonical bases, also called SAGBI bases, for subalgebras of the non-commutative polynomial ring are investigated. The process of subalgebra reduction is deened. Methods, including generalizations of the standard Grr obner bases techniques , are developed for the test whether bases are canoni-cal, and for the completion procedure of constructing canon-ical… (More)

Polynomial composition is the operation of replacing the variables in a polynomial with other polynomials. In this paper we give a sufficient and necessary condition on a set Θ of polynomials to assure that the set F • Θ of composed polynomials is a SAGBI basis whenever F is.

In this paper we introduce the concept of bi-automaton algebras, generalizing the automaton algebras previously defined by Ufnarovski. A bi-automaton algebra is a quotient of the free algebra, defined by a binomial ideal admitting a Gröbner basis which can be encoded as a regular set; we call such a Gröbner basis regular. We give several examples of… (More)

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