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单词 ArchimedeanSemigroup
释义

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.

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更新时间:2025/5/4 12:14:11