Injective Linear Cellular Automata and Sofic Groups
نویسندگان
چکیده
Let V be a finite-dimensional vector space over a field K and let G be a sofic group. We show that every injective linear cellular automaton τ : V G → V G is surjective. As an application, we obtain a new proof of the stable finiteness of group rings of sofic groups, a result previously established by G. Elek and A. Szabó using different methods.
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تاریخ انتشار 2007