A direct product decomposition of QMV algebras

被引：0
|
作者：
Xian Lu
Yun Shang
RuQian Lu
机构：
[1] Academy of Mathematics and Systems Science,Institute of Mathematics
[2] Chinese Academy of Sciences,Key Laboratory of Intelligent Information Processing, Institute of Computing Technology
来源：
Science China Mathematics | 2012年 / 55卷
关键词：
QMV algebra; commutativity; idempotent; decomposition theorem; 81P10; 03G12; 06C15;
D O I：
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学科分类号：
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：9
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