  It is well known that the ring of polynomial invariants of a reductive group
is finitely generated. However, it is difficult to give strong upper bounds on
the degrees of the generators, especially over fields of positive
characteristic. In this paper, we make use of the theory of good filtrations
along with recent results on the null cone to provide polynomial bounds for
matrix semi-invariants in arbitrary characteristic, and consequently for matrix
invariants. Our results generalize to invariants and semi-invariants of
quivers.
