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 

出　　处：《Science China Mathematics》2012年第4期841-850,共10页中国科学：数学（英文版）

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)

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 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.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：QMV algebra COMMUTATIVITY IDEMPOTENT decomposition theorem 

分 类 号：O153[理学—数学] O413.1[理学—基础数学]