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Abstract Let G be a group and let V be an algebraic variety over an algebraically closed field K. Let A denote the set of K -points of V. We introduce algebraic sofic subshifts AG and study endomorphisms. We generalize several results for dynamical invariant sets and nilpotency of that are well known for finite alphabet cellular automata. Under mild assumptions, we prove that is nilpotent if and only if its limit set, that is, the intersection of the images of its iterates, is a singleton. If moreover G is infinite, finitely generated and is topologically mixing, we show that is nilpotent if and only if its limit set consists of periodic configurations and has a finite set of alphabet values.
Ceccherini‐Silberstein et al. (Thu,) studied this question.