  We show that, for a fairly large class of reversible, one-dimensional
cellular automata, the set of additive invariants exhibits an algebraic
structure. More precisely, if $f$ and $g$ are one-dimensional, reversible
cellular automata of the kind considered by Takesue, we show that there is a
binary operation on these automata $\vee$ such that $\psi(f)\subseteq
\psi(f\vee g)$, where $\psi(f)$ denotes the set of additive invariants of $f$
and $\subseteq$ denotes the inclusion relation between real subspaces.
