Processing math: 100%

Abelian ordered groups

Abbreviation: AoGrp

Definition

An \emph{abelian ordered group} is an ordered group A=A,+,,0, such that

+ is commutative: x+y=y+x

Morphisms

Let A and B be abelian ordered groups. A morphism from A to B is a function h:AB that is an orderpreserving homomorphism: h(x+y)=h(x)+h(y) and xyh(x)h(y).

Examples

Example 1: Z,+,,0,, the integers with the usual ordering.

Basic results

Every ordered group with more than one element is infinite.

Properties

Finite members

None

Subclasses

Superclasses

References


QR Code
QR Code abelian_ordered_groups (generated for current page)