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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 Θ of non-commutative polynomials to assure that the set G ○ Θ of composed polynomials is a Gröbner basis in the free associative algebra whenever G is. The subject was initiated by Hong, treating the commutative analogue in (1998, J. Symb. Comput. 25, 643–663).
ACKNOWLEDGMENT
The author expresses his thanks to Victor Ufnarovski for inspiring discussions.