Characterization of homogeneity in orthocomplete atomic effect algebras

被引：6

作者：

Ji, Wei ^{[1
,2
]}

机构：

[1] Guilin Univ Technol, Coll Sci, Guilin 541004, Guangxi, Peoples R China

[2] Guilin Univ Technol, Guangxi Key Lab Spatial Informat & Geomat, Guilin 541004, Guangxi, Peoples R China

来源：

FUZZY SETS AND SYSTEMS | 2014年 / 236卷

基金：

中国国家自然科学基金;

关键词：

Effect algebra; Homogeneity; Basic decomposition of an element; Atomic decomposition; Sharp element; Smearing of a state; LATTICE EFFECT ALGEBRAS; ELEMENTS; BLOCKS; STATES; SHARP;

D O I：

10.1016/j.fss.2013.06.005

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove that homogeneity can be characterized by the decompositions of sharp elements in orthocomplete atomic effect algebras. Especially, an orthocomplete atomic effect algebra is homogeneous, if and only if the non-zero coefficient of an atom in any atomic decomposition of all sharp elements is the same, if and only if the non-zero coefficient of an atom in any atomic decomposition of the unit element is the same, which confirm the name "homogeneous". As an application, we prove the state smearing theorem for orthocomplete atomic homogeneous effect algebras. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：113 / 121

页数：9

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