Archimedean semigroup

Let S be a commutative semigroup. We say an element x divides an element y, written xy, if there is an element z such that xz=y.

An Archimedean semigroup S is a commutative semigroup with the property that for all x,yS there is a natural numberMathworldPlanetmath n such that xyn.

This is related to the Archimedean property of positive real numbers +: if x,y>0 then there is a natural number n such that x<ny. Except that the notation is additive rather than multiplicative, this is the same as saying that (+,+) is an Archimedean semigroup.

Title Archimedean semigroup
Canonical name ArchimedeanSemigroup
Date of creation 2013-03-22 13:08:06
Last modified on 2013-03-22 13:08:06
Owner mclase (549)
Last modified by mclase (549)
Numerical id 4
Author mclase (549)
Entry type Definition
Classification msc 20M14
Related topic ArchimedeanProperty
Defines divides
Defines ArchimedeanPlanetmathPlanetmath