Nordbeck, P. (2001). On the finiteness of Gröbner bases computation in quotients of the free algebra. *Applicable Algebra in Engineering, Communication and Computing*. Springer.

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Authors:

Nordbeck, Patrik

Department:

Mathematics (Faculty of Engineering)

Algebra

Algebra

Research Group:

Algebra

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.

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.

Keywords:

non-commutative algebras ;
Grobner bases ;
Dickson's lemma ;
Noetherianity ;
syzygies ;
POLYNOMIAL-RINGS

ISSN:

1432-0622

LUP-ID:

8baf3599-93f1-4097-b903-2cba6608ea0e | Link: https://lup.lub.lu.se/record/8baf3599-93f1-4097-b903-2cba6608ea0e
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