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On some basic applications of Gröbner bases in non-commutative polynomial rings

Nordbeck, Patrik LU (1998) 33 Years of Gröbner Bases 251. p.463-472
Abstract
In this paper we generalize some basic applications of Gröbner bases

in commutative polynomial rings to the non-commutative case. We define

a non-commutative elimination order. Methods

of finding the intersection of two ideals are given. If both the

ideals are monomial we deduce a finitely written basis for their intersection. We find the kernel of a

homomorphism, and decide membership of the image. Finally we show how to obtain a Gröbner basis for an

ideal by considering a related homogeneous ideal.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
London Math. Soc. Lecture Note Ser.
editor
Buchberger, Bruno and Winkler, Franz
volume
251
pages
463 - 472
publisher
Cambridge University Press
conference name
33 Years of Gröbner Bases
conference dates
1998-02-02
ISBN
0-521-63298-6
language
English
LU publication?
yes
id
ccc98c1c-45e1-40f8-aae2-b9bba835a21c (old id 1245329)
date added to LUP
2016-04-04 12:09:18
date last changed
2025-04-04 15:20:35
@inproceedings{ccc98c1c-45e1-40f8-aae2-b9bba835a21c,
  abstract     = {{In this paper we generalize some basic applications of Gröbner bases<br/><br>
in commutative polynomial rings to the non-commutative case. We define<br/><br>
a non-commutative elimination order. Methods<br/><br>
of finding the intersection of two ideals are given. If both the<br/><br>
ideals are monomial we deduce a finitely written basis for their intersection. We find the kernel of a<br/><br>
homomorphism, and decide membership of the image. Finally we show how to obtain a Gröbner basis for an<br/><br>
ideal by considering a related homogeneous ideal.}},
  author       = {{Nordbeck, Patrik}},
  booktitle    = {{London Math. Soc. Lecture Note Ser.}},
  editor       = {{Buchberger, Bruno and Winkler, Franz}},
  isbn         = {{0-521-63298-6}},
  language     = {{eng}},
  pages        = {{463--472}},
  publisher    = {{Cambridge University Press}},
  title        = {{On some basic applications of Gröbner bases in non-commutative polynomial rings}},
  volume       = {{251}},
  year         = {{1998}},
}