Non-commutative Grobner bases under composition

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 non-commutative polynomials to assure that the set G circle Theta of composed polynomials is a Grobner 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).