Ideals and congruence of distributive sequential effect algebra

doi:10.3778/j.issn.1002-8331.2009.25.006

Computer Engineering and Applications ›› 2009, Vol. 45 ›› Issue (25): 18-20.DOI: 10.3778/j.issn.1002-8331.2009.25.006

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Ideals and congruence of distributive sequential effect algebra

GUO Jian-sheng¹，LI Yong-ming^1,2

1.College of Mathematic and Information Science，Shaanxi Normal University，Xi’an 710062，China
2.College of Computer Science，Shaanxi Normal University，Xi’an 710062，China

Received:2009-03-27 Revised:2009-06-15 Online:2009-09-01 Published:2009-09-01
Contact: GUO Jian-sheng

分配序列效应代数的理想和同余

郭建胜¹，李永明^1,2

1.陕西师范大学数学与信息科学学院，西安 710062
2.陕西师范大学计算机科学学院，西安 710062

通讯作者: 郭建胜

Abstract

Abstract: A Distributive Sequential Effect Algebra（DSEA） is an effect algebra on which a distributive sequential product with natural properties is defined.Left ideal，right ideal，ideal，prime ideal and congruence in a distributive sequential effect algebra are introduced，and it is proved that every distributive sequential effect algebra（E；⊕，º 0，1） with the RDP having 1 as a product unity is a subdirect product of antilattice distributive sequential effect algebra with the RDP.

Key words: sequential effect algebra, distributive sequential effect algebra, ideal, congruence, subdirect proudct

摘要： 分配的序列效应代数（简记为DSEA），是指在一个效应代数上带有一种乘积运算并满足一定的条件。介绍了分配的序列效应代数中的左理想、右理想、理想、素理想和同余等概念，并且证明了满足（RDP）性质并且以1为乘积单位的分配序列效应代数是具有（RDP）性质的反格分配序列效应代数的子直积。

关键词: 序列效应代数, 分配序列效应代数, 理想, 同余, 子直积

CLC Number:

GUO Jian-sheng¹，LI Yong-ming^1,2. Ideals and congruence of distributive sequential effect algebra[J]. Computer Engineering and Applications, 2009, 45(25): 18-20.

郭建胜¹，李永明^1,2. 分配序列效应代数的理想和同余[J]. 计算机工程与应用, 2009, 45(25): 18-20.

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Ideals and congruence of distributive sequential effect algebra

分配序列效应代数的理想和同余

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