On algebraic cellular automata

Abstract

We investigate some general properties of algebraic cellular automata, i.e., cellular automata over groups whose alphabets are affine algebraic sets and which are locally defined by regular maps. When the ground field is assumed to be uncountable and algebraically closed, we prove that such cellular automata always have a closed image with respect to the prodiscrete topology on the space of configurations and that they are reversible as soon as they are bijective.

References in corpus (1)

• On the reversibility and the closed image property of linear cellular automata

Cited by in corpus (4)

• Invariant sets and nilpotency of endomorphisms of algebraic sofic shifts
• The Garden of Eden theorem: old and new
• On injective endomorphisms of symbolic schemes
• Standard decomposition of expansive ergodically supported dynamics