Indecomposable local maps of tessellation automata

Indecomposable local maps of one-dimensional tessellation automata are studied. The main results of this paper are the following. (1) For any alphabet containing two or more symbols and for anyn 1, there exist indecomposable scope-n local maps over . (2) If is a finite field of prime order, then a linear scope-n local map over is indecomposable if and only if its associated polynomial is an irreducible polynomial of degreen – 1 over , except for a trivial case. (3) Result (2) is no longer true if is a finite field whose order is not prime.