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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Authors:

Nordbeck, Patrik

Editors:

Buchberger, Bruno
;
Winkler, Franz

Department:

Mathematics (Faculty of Engineering)

Algebra

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.

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
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