序列效应代数的Holland理论

doi:10.3778/j.issn.1002-8331.2010.27.007

计算机工程与应用 ›› 2010, Vol. 46 ›› Issue (27): 29-31.DOI: 10.3778/j.issn.1002-8331.2010.27.007

序列效应代数的Holland理论

郭建胜

陕西师范大学数学与信息科学学院，西安 710062

收稿日期:2010-06-22 修回日期:2010-08-11 出版日期:2010-09-21 发布日期:2010-09-21
通讯作者: 郭建胜

Holland’s theory for sequential effect algebras

GUO Jian-sheng

College of Mathematic and Information Science，Shaanxi Normal University，Xi’an 710062，China

Received:2010-06-22 Revised:2010-08-11 Online:2010-09-21 Published:2010-09-21
Contact: GUO Jian-sheng

摘要/Abstract

摘要： 介绍了序列效应代数的概念，给出了交换的序列效应代数的一些性质，证明了交换的序列效应代数由素理想诱导的商代数仍然是交换的序列效应代数。最后证明了每一个交换的序列效应代数能被表示为某个反格的自态射形成的序列效应代数。这样的表示是有用的，因为它给出了一个交换的序列效应代数作为自态射的集合的具体化。

关键词: 序列效应代数, 反格, 素理想, 自态射

Abstract: The definition of sequential effect algebras is introduced and some character of sequential effect algebras are given.It is proved that the quotient algebra induced by a prime ideal of a commutative sequential effect algebra is also a commutative sequential effect algebra.It is showed that every commutative sequential effect algebra can be represented by the commutative sequential effect algebra of automorphisms of an antilattice. Such a representation is useful since it gives a visualization of some commutative sequential effect algebra as a set of automorphisms.

Key words: sequential effect algebra, antilattice, prime ideal, automorphism

中图分类号:

郭建胜. 序列效应代数的Holland理论[J]. 计算机工程与应用, 2010, 46(27): 29-31.

GUO Jian-sheng. Holland’s theory for sequential effect algebras[J]. Computer Engineering and Applications, 2010, 46(27): 29-31.

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序列效应代数的Holland理论

Holland’s theory for sequential effect algebras

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