Direct topological factorization for topological flows

This paper considers the general question of when a topological action of a countable group can be factored into a direct product of non-trivial actions. In the early 1980s, D. Lind considered such questions for Z-shifts of finite type. In particular, we study direct factorizations of subshifts of finite type over Z^d and other groups, and Z-subshifts which are not of finite type. The main results concern direct factors of the multidimensional full n-shift, the multidimensional -colored chessboard and the Dyck shift over a prime alphabet. A direct factorization of an expansive G-action must be finite, but an example is provided of a non-expansive Z-action for which there is no finite direct-prime factorization. The question about existence of direct-prime factorization of expansive actions remains open, even for G = Z.