Category:Definitions/Quotient Structures

This category contains definitions related to Quotient Structures.
Related results can be found in Category:Quotient Structures.

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 $\RR$.

Let $\circ_\RR$ be the operation induced on $S / \RR$ by $\circ$.

The quotient structure defined by $\RR$ is the algebraic structure:

$\struct {S / \RR, \circ_\RR}$