Page "Invariant theory" Paragraph 17

for some a < sub > j </ sub > in the ring R because x is in the ideal I.

We can assume that a < sub > j </ sub > is homogeneous of degree d − deg i < sub > j </ sub > for every j ( otherwise, we replace a < sub > j </ sub > by its homogeneous component of degree d − deg i < sub > j </ sub >; if we do this for every j, the equation x =