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- Patrik Nordbeck
- 1998

In this paper we generalize some basic applications of Grr obner bases in commutative polynomial rings to the non-commutative case. We deene a non-commutative elimination order. Methods of nding the intersection of two ideals are given. If both the ideals are monomial we deduce a nitely written basis for their intersection. We nd the kernel of a… (More)

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 canonical, and for the completion procedure of constructing canonical… (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.

- Patrik Nordbeck
- 2001

Polynomial composition is the operation of replacing the variables in a polynomial with other polynomials. In this paper we give sufficient and necessary conditions on a set Y of non-commutative polynomials to assure that the set G + Y of composed polynomials is a Gro¨bner basis in the free asso-ciative algebra whenever G is. The subject was initiated by… (More)

- P. Nordbeck
- 1999

We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. The usual theory for Gröbner bases and its counterpart for subalge-bras of polynomial rings, also called SAGBI bases, are combined to obtain a tool for computation in subalgebras of factor algebras.

Preface " Trying is the first step towards failure. " Homer Simpson This thesis deals with computational methods in algebra, mainly focusing on the concept of Gröbner and SAGBI bases in non-commutative algebras. The theory of these bases is constructive in the meaning that the purpose is to provide methods for solving specific problems. As the reader will… (More)

- Patrik Nordbeck
- 2007

We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. A more complete exposition can be found in 4]. Canonical bases for subalgebras of the commutative polynomial ring were introduced by Kapur and Madlener (see 2]), and independently by Robbiano and Sweedler ((5]). Some notes on the non-commutative… (More)

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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