NON-COMMUTATIVE GRÖBNER BASES UNDER COMPOSITION
Patrik Nordbeck · Communications in Algebra · 2001
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 Y of non-commutative polynomials to assure that the set G + Y 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).