Institute of Computing Technology, Chinese Academy IR
A direct product decomposition of QMV algebras | |
Lu Xian1; Shang Yun1; Lu RuQian2 | |
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. |
条目包含的文件 | 条目无相关文件。 |
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