Computing restrictions of ideals in finitely generated k-algebras by means of Buchberger’s algorithm

Gröbner bases can be used to solve various algorithmic problems in the context of finitely generated field extensions. One key idea is the computation of a certain kind of restriction of an ideal to a subring. With this restricted ideal many problems concerning function fields reduce to ideal theoretic problems which can be solved by means of Buchberger’s algorithm. In this contribution this approach is generalized to allow the computation of the restriction of an arbitrary ideal to a subring.