一类效应代数中的理想

IDEALS OF A CLASS OF EFFECT ALGEBRAS

证明了若I是效应代数(E(Ω),,⊥,0,1)的一个闭理想,则存在Ω的一个闭的子集S,使得I是所有在S上为零的函数的集合.反之,若S是一个Ω的闭子集,则所有在S上为零的函数之集是效应代数(E(Ω),,⊥,0,1)的一个闭理想.

In this paper,the ideals of a class of effect algebras were studied.It is proved that if I is a closed ideal in（E（Ω）,,⊥,0,1）,then there is a closed subset S of Ω that I is the set of all functions vanishing on S,and that if S is a closed subset of Ω,the set of all functions vanishing on S is a closed ideal in（E（Ω）,,⊥,0,1）.