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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)

- Patrik Nordbeck
- ISSAC
- 1998

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

- Patrik Nordbeck
- J. Symb. Comput.
- 2002

Our interest in the subject of this paper is inspired by Hong (1998), where Hoon Hong addresses the problem of the behavior of Gröbner bases under composition of polynomials. More precisely, let Θ be a set of polynomials, as many as the variables in our polynomial ring. The question then is under which conditions on these polynomials it is true that for an… (More)

- Patrik Nordbeck
- The Computer Science Journal of Moldova
- 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 subalgebras of polynomial rings, also called SAGBI bases, are combined to obtain a tool for computation in subalgebras of factor algebras.

We investigate, for quotients of the non-commutative polynomial ring, a property that implies finiteness of Gröbner bases computation, and examine its connection with Noetherianity. We propose a Gröbner bases theory for our factor algebras, of particular interest for one-sided ideals, and show a few applications, e.g. how to compute (one-sided) syzygy… (More)

- Jonas Månsson, Patrik Nordbeck
- J. Symb. Comput.
- 2002

In Ufnarovski (1989), the concept of automaton algebras is introduced. These are quotients of the non-commutative polynomial ring where the defining ideal allows some Gröbner basis with a regular set of leading words. However, nothing is reflected concerning the whole structure of the Gröbner basis (except of course for monomial algebras). In this paper we… (More)

- Patrik Nordbeck
- Applicable Algebra in Engineering, Communication…
- 2001

We investigate, for quotients of the non-commutative polynomial ring, a property that implies finiteness of Gröbner bases computation, and examine its connection with Noetherianity. We propose a Gröbner bases theory for our factor algebras, of particular interest for one-sided ideals, and show a few applications, e.g. how to compute (one-sided) syzygy… (More)

- Jonas Månsson, Patrik Nordbeck
- Applicable Algebra in Engineering, Communication…
- 2005

An important tool for studying standard finitely presented algebras is the Ufnarovski graph. In this paper we extend the use of the Ufnarovski graph to automaton algebras, introducing the generalized Ufnarovski graph. As an application, we show how this construction can be used to test Noetherianity of automaton algebras.

- 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)

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