Distributivity

algebra

Definition

Distributivity

Let $R_1,R_2$ be two binary relations (often operations) on a set $S$.

Left Distributivity: $R_1$ is left distributive over $R_2$ if

$$\forall x,y,z\in S:x{R}_1(y{R}_{2}z)=(x{R}_{1}y)R_2(x{R}_{1}z).$$

Right Distributivity: $R_1$ is right distributive over $R_2$ if

$$\forall x,y,z\in S:(y{R}_{2}z)R_{1}x=(y{R}_{1}x)R_2(z{R}_{1}x).$$