# nLab totally ordered abelian group

Contents

### Context

#### Algebra

higher algebra

universal algebra

(0,1)-category

(0,1)-topos

# Contents

## Idea

A totally ordered abelian group is an ordered abelian group whose order forms a total order.

## Definition

The following definition is from Peter Freyd:

A totally ordered abelian group is an pseudolattice ordered abelian group $G$ such that for all elements $a$ in $G$, $a \leq 0$ or $-a \leq 0$.

In a totally ordered abelian group, the join is usually called the maximum, while the meet is usually called the minimum

## Examples

The integers, the rational numbers, and the real numbers are totally ordered abelian groups.

## References

• Peter Freyd, Algebraic real analysis, Theory and Applications of Categories, Vol. 20, 2008, No. 10, pp 215-306 (tac:20-10)

Created on June 18, 2021 at 17:46:10. See the history of this page for a list of all contributions to it.