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totally ordered abelian group

Contents

Context

Algebra

(0,1)-Category theory

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 GG such that for all elements aa in GG, a0a \leq 0 or a0-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.