Non-commutative Gröbner bases under composition

Nordbeck, P. (2001). Non-commutative Gröbner bases under composition. Communications in Algebra. Taylor & Francis.
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| Published | English
Authors:
Nordbeck, Patrik
Department:
Mathematics (Faculty of Engineering)
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).
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 | Statistics

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