Non-commutative Gröbner bases under composition

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Bibtex

@article{74882e86fb0e4fabaf363e823554c753,
title = "Non-commutative Gr{\"o}bner bases under composition",
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 Gr{\"o}bner 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",
author = "Patrik Nordbeck",
year = "2001",
doi = "10.1081/AGB-100106789",
language = "English",
volume = "29",
pages = "4831--4851",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor & Francis",
number = "11",

}