Definition:Relation Compatible with Operation

Definition
Let $\mathcal R$ be a relation on an algebraic structure $\left({S, \circ}\right)$.

Then $\mathcal R$ is compatible with $\circ$ iff:


 * $\forall x_1, x_2, y_1, y_2 \in S: x_1 \mathcal R x_2 \land y_1 \mathcal R y_2 \implies \left({x_1 \circ y_1}\right) \mathcal R \left({x_2 \circ y_2}\right)$

Also see

 * Congruence relation