Distributivity

algebra

Definition

Distributivity

Left Distributivity: Two relations $R_1,R_2$ are called left distributive over a set $S$ if:

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

Right Distributivity: Two relations $R_1,R_2$ are called right distributive over a set $S$ if:

$$\forall x,y,z\in S:(x{R}_{2}y)R_{1}z=(x{R}_{2}z)R_1(y{R}_{2}z)$$