The first bound for syzygies (as well as for ideal membership problem) was given in 1926 by Grete Hermann: Let a submodule of a free module of dimension over formula_54 if the coefficients over a basis of of a generating system of have a total degree at most , then there is a constant such that the degrees occurring in a generating system of the first syzygy module is at most formula_55 The same bound applies for testing the membership to of an element of .