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.
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
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)
