On images of subshifts under embeddings of symbolic varieties

Abstract We show that the image of a subshift X under various injective morphisms symbolic algebraic varieties over monoid universes with variety alphabets is finite type, respectively sofic subshift, if and only so . Similarly, let G be countable A , B Artinian modules ring. prove for every closed submodule $\Sigma \subset A^G$ -equivariant uniformly continuous module homomorphism $\tau \colon \! \Sigma \to B^G$ $\Delta $ sofic, (\Delta )$ Generalizations admissible group cellular automata structure are also obtained.