Let $S$ be the set of maps and $\phi,\psi \in S$. Let $x,y \in \mathbb{Z}$. Suppose that $\phi(x) * \psi(y) = \nu(xy)$ for some $\nu \in S$. Then what would you call such a system of maps?
If that was easy, then what would you call such as system if all of the maps are only partially defined on $\mathbb{Z}$?
Note: $xy$ is the integer product, and $*$ is some binary operator on $\{\phi(x) : x \in \mathbb{Z}, \phi\in S\}$
Grazie.