Rings of matrix invariants in positive characteristic

Denote by Rn,m the ring of invariants of m-tuples of n×n matrices (m,n 2) over an infinite base field K under the simultaneous conjugation action of the general linear group. When char(K)=0, Razmyslov (Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974) 723) and Procesi (Adv. Math. 19 (1976) 306) established a connection between the Nagata–Higman theorem and the degree bound for generators of Rn,m. We extend this relationship to the case when the base field has positive characteristic. In particular, we show that if 0