具有尖元完备格的阿基米德原子格效应代数
Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
摘要：
研究了锐元集为完备格的阿基米德原子格效应代数。给出了这种格效应代数的中心、相容中心和中心原子的性质。证明了如果这种效应代数$E$是可分模的，则在$E$上存在一个忠实态.进一步地，如果原子格效应代数可稠密嵌入到完备格效应代数$\widehat{E}$中，且$E$的相容中心不是布尔代数，则在$E$上存在$(o)$ -连续次可加态.
英文摘要：
We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras. Moreover, we prove that if such effect algebra $E$ is separable and modular then there exists a faithful state on $E$. Further, if an atomic lattice effect algebra is densely embeddable into a complete lattice effect algebra $\widehat{E}$ and the compatiblity center of $E$ is not a Boolean algebra then there exists an $(o)$-continuous subadditive state on $E$.
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