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

Patrik Nordbeck

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

Matematik LTH

Forskningsoutput: Kapitel i bok/rapport/Conference proceeding › Konferenspaper i proceeding › Peer review

Sammanfattning

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.

Originalspråk	engelska
Titel på värdpublikation	London Math. Soc. Lecture Note Ser.
Redaktörer/författare	Bruno Buchberger, Franz Winkler
Förlag	Cambridge University Press
Sidor	463-472
Volym	251
ISBN (tryckt)	0-521-63298-6
Status	Published - 1998
Evenemang	33 Years of Gröbner Bases - Linz Varaktighet: 1998 feb. 2 → …

Publikationsserier

Namn
Volym	251

Konferens

Konferens	33 Years of Gröbner Bases
Period	1998/02/02 → …

Ämnesklassifikation (UKÄ)

Matematik

Algebra
Meurman, A. (Forskare), Månsson, J. (Forskare), Nordbeck, P. (Forskare), Torstensson, A. (Forskare) & Ufnarovski, V. (Forskare)
1982/01/01 → …
Projekt: Forskning

Citera det här

@inproceedings{ccc98c1c45e140f8aae2b9bba835a21c,

title = "On some basic applications of Gr{\"o}bner bases in non-commutative polynomial rings",

abstract = "In this paper we generalize some basic applications of Gr{\"o}bner 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 Gr{\"o}bner basis for an ideal by considering a related homogeneous ideal.",

author = "Patrik Nordbeck",

year = "1998",

language = "English",

isbn = "0-521-63298-6",

volume = "251",

publisher = "Cambridge University Press",

pages = "463--472",

editor = "Bruno Buchberger and Franz Winkler",

booktitle = "London Math. Soc. Lecture Note Ser.",

address = "United Kingdom",

note = "33 Years of Gr{\"o}bner Bases ; Conference date: 02-02-1998",

}

TY - GEN

T1 - On some basic applications of Gröbner bases in non-commutative polynomial rings

AU - Nordbeck, Patrik

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

M3 - Paper in conference proceeding

SN - 0-521-63298-6

VL - 251

SP - 463

EP - 472

BT - London Math. Soc. Lecture Note Ser.

A2 - Buchberger, Bruno

A2 - Winkler, Franz

PB - Cambridge University Press

T2 - 33 Years of Gröbner Bases

Y2 - 2 February 1998

ER -

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

Sammanfattning

Publikationsserier

Konferens

Ämnesklassifikation (UKÄ)

Fingeravtryck

Projekt

Algebra

Citera det här