# Category:Quotient Structures

Jump to navigation
Jump to search

This category contains results about Quotient Structures.

Let $\left({S, \circ}\right)$ be an algebraic structure.

Let $\mathcal R$ be a congruence relation on $\left({S, \circ}\right)$.

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

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

The **quotient structure defined by $\mathcal R$** is the algebraic structure:

- $\left({S / \mathcal R, \circ_\mathcal R}\right)$

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### Q

## Pages in category "Quotient Structures"

The following 10 pages are in this category, out of 10 total.

### Q

- Quotient Mapping on Structure is Canonical 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
- Quotient Theorem for Epimorphisms