Non-commutative Gröbner bases under composition

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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).

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Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • non-commutative Grobner bases, composition of polynomials
Original languageEnglish
Pages (from-to)4831-4851
JournalCommunications in Algebra
Volume29
Issue number11
Publication statusPublished - 2001
Publication categoryResearch
Peer-reviewedYes