# Category:Quotient Structures

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This category contains results about **Quotient Structures**.

Definitions specific to this category can be found in Definitions/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:

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

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Quotient Structures"

The following 13 pages are in this category, out of 13 total.

### E

### Q

- Quotient Mapping on Structure is Epimorphism
- Quotient Structure is Similar to Structure
- Quotient Structure is Well-Defined
- Quotient Structure of Abelian Group is Abelian Group
- Quotient Structure of Group is Group
- Quotient Structure of Inverse Completion
- Quotient Structure of Monoid is Monoid
- Quotient Structure of Semigroup is Semigroup
- Quotient Structure on Subset Product