Ergodic endomorphisms of compact abelian groups

We show that for a surjective endomorphism of a compact abelian group ergodicity is equivalent to a condition which impliesr-mixing for allr1, and we characterize such maps algebraically. This is then used in proving the ergodicity of an extensive class of endomorphisms of the binary sequence space. As a simple corollary it is found that one-dimensional linear cellular automata and the accumulator automata arer-mixing for allr1.This work was supported in part by grants from NSERC