Abstract
Let V be a finite-dimensional vector space over a field \(\mathbb{K}\) and let G be a sofic group. We show that every injective linear cellular automaton τ: VG → VG 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. Szabo using different methods.
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