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Amenability and Linear Cellular Automata Over Semisimple Modules of Finite Length |
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| Authors: | Tullio Ceccherini-Silberstein Michel Coornaert |
| Affiliation: | 1. Dipartimento di Ingegneria , Universitá del Sannio , Benevento, Italy tceccher@mat.uniroma1.it;3. Institute de Recherche Mathématique Avancée, Université Louis Pasteur and CNRS , Strasbourg, France |
| Abstract: | Let M be a semisimple left module of finite length over a ring R and let G be an amenable group. We show that an R-linear cellular automaton τ:MG → MG is surjective if and only if it is pre-injective. |
| Keywords: | Amenable group Artinian module Linear cellular automaton Module of finite length Noetherian module Pre-injectivity Semisimple module |