A direct product decomposition of QMV algebras

作     者：LU Xian 1 ,SHANG Yun 1,& LU RuQian 1,2 1 Institute of Mathematics,Academy of Mathematics and Systems Science,Beijing 100190,China 2 Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences,Beijing 100190,China 

作者机构：Institute of Mathematics Academy of Mathematics and Systems Science Beijing China Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2012年第55卷第4期

页      面：841-850页

核心收录：

学科分类：07[理学] 0809[工学-电子科学与技术（可授工学、理学学位）] 070205[理学-凝聚态物理] 08[工学] 070104[理学-应用数学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 60736011, 61073023 and 60603002) the National Basic Research Program of China (973 Program) (Grant No. 2009CB320701) 

主　　题：QMV algebra commutativity idempotent decomposition theorem 

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 idempo- tent 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 *** 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 *** also generalizes the cases of orthomodular lattices.