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On the finiteness of Gröbner bases computation in quotients of the free algebra

Nordbeck, Patrik LU (2001) In Applicable Algebra in Engineering, Communication and Computing 11(3). p.157-180
Abstract
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 modules.
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 algebras, Grobner bases, Dickson's lemma, Noetherianity, syzygies, POLYNOMIAL-RINGS
in
Applicable Algebra in Engineering, Communication and Computing
volume
11
issue
3
pages
157 - 180
publisher
Springer
external identifiers
  • scopus:0035070396
ISSN
1432-0622
DOI
10.1007/s002000000045
language
English
LU publication?
yes
id
8baf3599-93f1-4097-b903-2cba6608ea0e (old id 1245204)
alternative location
http://www.springerlink.com/content/mlwe4gqth788yd6h/fulltext.pdf
date added to LUP
2008-10-20 09:22:10
date last changed
2018-05-29 12:10:30
@article{8baf3599-93f1-4097-b903-2cba6608ea0e,
  abstract     = {We investigate, for quotients of the non-commutative polynomial<br/><br>
 ring, a property that implies finiteness of Gröbner bases<br/><br>
 computation, and examine its connection with Noetherianity.<br/><br>
 We propose a Gröbner bases theory for our factor algebras, of particular interest for <br/><br>
 one-sided ideals, and show a few<br/><br>
 applications, e.g. how to compute (one-sided) syzygy modules.},
  author       = {Nordbeck, Patrik},
  issn         = {1432-0622},
  keyword      = {non-commutative algebras,Grobner bases,Dickson's lemma,Noetherianity,syzygies,POLYNOMIAL-RINGS},
  language     = {eng},
  number       = {3},
  pages        = {157--180},
  publisher    = {Springer},
  series       = {Applicable Algebra in Engineering, Communication and Computing},
  title        = {On the finiteness of Gröbner bases computation in quotients of the free algebra},
  url          = {http://dx.doi.org/10.1007/s002000000045},
  volume       = {11},
  year         = {2001},
}