# Non-commutative Gröbner bases under composition

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**Non-commutative Gröbner bases under composition.** / Nordbeck, Patrik.

Research output: Contribution to journal › Article

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*Communications in Algebra*, vol. 29, no. 11, pp. 4831-4851. https://doi.org/10.1081/AGB-100106789

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*Communications in Algebra*,

*29*(11), 4831-4851. https://doi.org/10.1081/AGB-100106789

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*Communications in Algebra*. 2001, 29(11). 4831-4851. https://doi.org/10.1081/AGB-100106789

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TY - JOUR

T1 - Non-commutative Gröbner bases under composition

AU - Nordbeck, Patrik

PY - 2001

Y1 - 2001

N2 - 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).

AB - 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).

KW - non-commutative Grobner bases

KW - composition of polynomials

U2 - 10.1081/AGB-100106789

DO - 10.1081/AGB-100106789

M3 - Article

VL - 29

SP - 4831

EP - 4851

JO - Communications in Algebra

T2 - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 11

ER -