Define for [[Operation]]. **Definition** Given two [[Binary Operation]] $*$ and $+$ on a set $S$, - the operation $*$ is *left-distributive* over (or *wrt*) $+$ if for any $x,y,z\in S$ $x*(y+z)=(x*y)+(x*z);$ - the operation $*$ is *right-distributive* over (or *wrt*) $+$ if for any $x,y,z\in S$ $(y+z)*x=(y*x)+(z*x);$ - and the operation $*$ is *distributive* over $+$ if it is both left and right distributive wrt $+$. **Remark** Note that for the reals, division is only right-distributive over addition.