Distributive Property - Definition

Definition

Given a set S and two binary operators · and + on S, we say that the operation ·

• is left-distributive over + if, given any elements x, y, and z of S,

x · (y + z) = (x · y) + (x · z);

• is right-distributive over + if, given any elements x, y, and z of S:

(y + z) · x = (y · x) + (z · x);

• is distributive over + if it is left- and right-distributive.

Notice that when · is commutative, then the three above conditions are logically equivalent.