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Non-commutative Gröbner bases under composition

Nordbeck, Patrik LU (2001) In Communications in Algebra 29(11). p.4831-4851
Abstract
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 $Theta$ of noncommutative polynomials to assure that the set $G circ Theta$ of composed polynomials is a Gröbner basis in the free associative algebra whenever $G$ is. The subject was initiated by H. Hong, who treated the commutative analogue in (J. Symbolic Comput. 25 (1998), no. 5, 643--663).
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
non-commutative Grobner bases, composition of polynomials
in
Communications in Algebra
volume
29
issue
11
pages
4831 - 4851
publisher
Taylor & Francis
external identifiers
  • scopus:0035598122
ISSN
0092-7872
DOI
10.1081/AGB-100106789
language
English
LU publication?
yes
id
74882e86-fb0e-4fab-af36-3e823554c753 (old id 1245202)
alternative location
http://pdfserve.informaworld.com/986501_731396340_713729597.pdf
date added to LUP
2008-10-20 09:24:35
date last changed
2018-05-29 10:55:27
@article{74882e86-fb0e-4fab-af36-3e823554c753,
  abstract     = {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 $Theta$ of noncommutative polynomials to assure that the set $G circ Theta$ of composed polynomials is a Gröbner basis in the free associative algebra whenever $G$ is. The subject was initiated by H. Hong, who treated the commutative analogue in (J. Symbolic Comput. 25 (1998), no. 5, 643--663).},
  author       = {Nordbeck, Patrik},
  issn         = {0092-7872},
  keyword      = {non-commutative Grobner bases,composition of polynomials},
  language     = {eng},
  number       = {11},
  pages        = {4831--4851},
  publisher    = {Taylor & Francis},
  series       = {Communications in Algebra},
  title        = {Non-commutative Gröbner bases under composition},
  url          = {http://dx.doi.org/10.1081/AGB-100106789},
  volume       = {29},
  year         = {2001},
}