计算机工程与应用 ›› 2009, Vol. 45 ›› Issue (25): 18-20.DOI: 10.3778/j.issn.1002-8331.2009.25.006

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分配序列效应代数的理想和同余

郭建胜1,李永明1,2   

  1. 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
  • 收稿日期:2009-03-27 修回日期:2009-06-15 出版日期:2009-09-01 发布日期:2009-09-01
  • 通讯作者: 郭建胜

Ideals and congruence of distributive sequential effect algebra

GUO Jian-sheng1,LI Yong-ming1,2   

  1. 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

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

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

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