A direct product decomposition of QMV algebras

	A direct product decomposition of QMV algebras
	Lu Xian 1; Shang Yun 1; Lu RuQian 2
	2012
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	55 期号:4 页码:841
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.
关键词	QUANTUM MV-ALGEBRAS QMV algebra commutativity idempotent decomposition theorem
语种	英语
资助项目	[National Natural Science Foundation of China] ; [National Basic Research Program of China (973 Program)]
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/35526
专题	中国科学院计算技术研究所期刊论文_中文
作者单位	1.中国科学院系统科学研究所 2.中国科学院计算技术研究所
推荐引用方式 GB/T 7714	Lu Xian,Shang Yun,Lu RuQian. A direct product decomposition of QMV algebras[J]. SCIENCE CHINA-MATHEMATICS,2012,55(4):841.
APA	Lu Xian,Shang Yun,&Lu RuQian.(2012).A direct product decomposition of QMV algebras.SCIENCE CHINA-MATHEMATICS,55(4),841.
MLA	Lu Xian,et al."A direct product decomposition of QMV algebras".SCIENCE CHINA-MATHEMATICS 55.4(2012):841.