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

Nordbeck, Patrik (1998). On some basic applications of Gröbner bases in non-commutative polynomial rings. Buchberger, Bruno; Winkler, Franz (Eds.). , 251,, 463 - 472. 33 Years of Gröbner Bases. Linz: Cambridge University Press
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Conference Proceeding/Paper | Published | English
Authors:
Nordbeck, Patrik
Editors:
Buchberger, Bruno ; Winkler, Franz
Department:
Mathematics (Faculty of Engineering)
Algebra
Research Group:
Algebra
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.
ISBN:
0-521-63298-6
LUP-ID:
ccc98c1c-45e1-40f8-aae2-b9bba835a21c | Link: https://lup.lub.lu.se/record/ccc98c1c-45e1-40f8-aae2-b9bba835a21c | Statistics

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