An Easily Checkable Algebraic Characterization of Positive Expansivity for Additive Cellular Automata over a Finite Abelian Group

We provide an easily checkable algebraic characterization of positive expansivity for Additive Cellular Automata over a finite abelian group. First of all, an easily checkable characterization of positive expansivity is provided for the non trivial subclass of Linear Cellular Automata over the alphabet $(\mathbb{Z}\mathrm{/}m\mathbb{Z}{)}^n$. Then, we show how it can be exploited to decide positive expansivity for the whole class of Additive Cellular Automata over a finite abelian group.