A direct product decomposition of QMV algebras

被引：0
|
作者：
Lu Xian [1 ]
Shang Yun [1 ]
Lu RuQian [1 ,2 ]
机构：
[1] Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
[2] Chinese Acad Sci, Inst Comp Technol, Key Lab Intelligent Informat Proc, Beijing 100190, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2012年 / 55卷 / 04期
基金：
中国国家自然科学基金;
关键词：
QMV algebra; commutativity; idempotent; decomposition theorem; QUANTUM MV-ALGEBRAS;
D O I：
10.1007/s11425-011-4310-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the direct product decomposition of quantum many-valued algebras (QMV algebras) which generalizes the decomposition theorem of ortholattices (orthomodular lattices). In detail, for an idempotent element of a given QMV algebra, if it commutes with every element of the QMV algebra, it can induce a direct product decomposition of the QMV algebra. At the same time, we introduce the commutant C(S) of a set S in a QMV algebra, and prove that when S consists of idempotent elements, C(S) is a subalgebra of the QMV algebra. This also generalizes the cases of orthomodular lattices.
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页码：841 / 850
页数：10
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