Nordbeck, P., 2001. Non-commutative Gröbner bases under composition. *Communications in Algebra*, 29(11), pp.4831 – 4851.

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Authors:

Nordbeck, Patrik

Department:

Mathematics (Faculty of Engineering)

Algebra

Algebra

Research Group:

Algebra

Abstract:

Polynomial composition is the operation of replacing the variables in a polynomial with other polynomials. In this paper we give sufficient and necessary conditions on a set $Theta$ of noncommutative polynomials to assure that the set $G circ Theta$ of composed polynomials is a Gröbner basis in the free associative algebra whenever $G$ is. The subject was initiated by H. Hong, who treated the commutative analogue in (J. Symbolic Comput. 25 (1998), no. 5, 643--663).

Polynomial composition is the operation of replacing the variables in a polynomial with other polynomials. In this paper we give sufficient and necessary conditions on a set $Theta$ of noncommutative polynomials to assure that the set $G circ Theta$ of composed polynomials is a Gröbner basis in the free associative algebra whenever $G$ is. The subject was initiated by H. Hong, who treated the commutative analogue in (J. Symbolic Comput. 25 (1998), no. 5, 643--663).

Keywords:

non-commutative Grobner bases ;
composition of polynomials

ISSN:

0092-7872

LUP-ID:

74882e86-fb0e-4fab-af36-3e823554c753 | Link: https://lup.lub.lu.se/record/74882e86-fb0e-4fab-af36-3e823554c753
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