Definition:Operation Induced on Quotient Set

Definition
Let $\struct {S, \circ}$ be an algebraic structure.

Let $\RR$ be a congruence relation on $\struct {S, \circ}$.

Let $S / \RR$ be the quotient set of $S$ by $\RR$.

The operation $\circ_\RR$ induced on $S / \RR$ by $\circ$ is defined as:


 * $\eqclass x \RR \circ_\RR \eqclass y \RR = \eqclass {x \circ y} \RR$

Also see

 * Definition:Quotient Structure
 * Quotient Structure is Well-Defined