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

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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.
Original languageEnglish
Title of host publicationLondon Math. Soc. Lecture Note Ser.
EditorsBruno Buchberger, Franz Winkler
PublisherCambridge University Press
Pages463-472
Volume251
ISBN (Print)0-521-63298-6
Publication statusPublished - 1998
Event33 Years of Gröbner Bases - Linz
Duration: 1998 Feb 2 → …

Publication series

Name
Volume251

Conference

Conference33 Years of Gröbner Bases
Period1998/02/02 → …

Subject classification (UKÄ)

  • Mathematics

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