具有Riesz分解性质的广义效应代数-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

具有Riesz分解性质的广义效应代数

颉永建

(陕西师范大学数学与信息科学学院，陕西西安 710062)

颉永建,男,博士研究生,研究方向为量子逻辑 E-mail:yjxie@snnu.edu.cn.

摘要:

研究了上定向的具有Riesz分解性质的广义效应代数的结构.引入了广义效应代数中素理想的定义，证明了上定向的具有Riesz分解性质的广义效应代数是有限次直既约的当且仅当它是反格；上定向的具有Riesz分解性质的广义效应代数通过理想得到的商代数是反格当且仅当此理想是素理想. 最后证明了上定向的具有Riesz分解性质的广义效应代数具有子直积表示.

关键词：

量子逻辑; 广义效应代数; Riesz理想; 素理想; 同余关系

收稿日期：

2009-02-17

中图分类号：

O153.1; O152.2

文献标识码：

文章编号：

1672-4291(2009)03-0001-04

基金项目：

国家自然科学基金资助项目(60873119)；教育部高等学校博士点基金资助项目(200807180005)

Doi:

Generalized effect algebras with Riesz decomposition property

XIE Yong-jian

(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)

Abstract:

The structures of upwards directed generalized effect algebras with Riesz decomposition property are studied. The definition of prime ideal in a generalized effect algebra is introduced. It is proved that an upwards directed generalized effect algebra with Riesz decomposition property is finitely subdirectly irreducible if and only if it is an antilattice. Then it is shown that a quotient of an upwards directed generalized effect algebra with Riesz decomposition property is an antilattice if and only if the ideal inducing that quotient is prime. At last, it is proved that every upwards directed generalized effect algebra with Riesz decomposition property has a subdirect product representation.

KeyWords:

quantum logic; generalized effect algebra; Riesz ideal; prime ideal; congruence