Computing Gröbner Bases by FGLM Techniques in a Non-commutative Setting

A generalization of the FGLM technique is given to compute Gröbner bases for two-sided ideals of free finitely generated algebras. Specializations of this algorithm are presented for the cases in which the ideal is determined by either functionals or monoid (group) presentations. Generalizations are discussed in order to compute Gröbner bases on (twisted) semigroup rings.