Generating infinite monoids of cellular automata

For a group $G$ and set $A$, let $\text{End}(A^G)$ be the monoid of all cellular automata over $A^G$, $\text{Aut}(A^G)$ its units. By establishing characterisation surjunctuve groups in terms $\text{End}(A^G)$, we prove that rank (i.e. smallest cardinality generating set) is equal to plus relative latter infinite when has an decreasing chain normal subgroups finite index, condition which satisfied, for example, any residually group. Moreover, $A=V$ vector space field $\mathbb{F}$, study $\text{End}_{\mathbb{F}}(V^G)$ linear $V^G$ units $\text{Aut}_{\mathbb{F}}(V^G)$. We show if indicable $V$ finite-dimensional, then not finitely generated; however, generated $G$, $\text{Aut}_{\mathbb{F}}(\mathbb{F}^G)$ only $\mathbb{F}$ finite.