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Keywords:
lattice effect algebra; sharp and central element; block; state; subdirect decomposition; MacNeille completion
lattice effect algebra; sharp and central element; block; state; subdirect decomposition; MacNeille completion
Summary:
We prove that every Archimedean atomic lattice effect algebra the center of which coincides with the set of all sharp elements is isomorphic to a subdirect product of horizontal sums of finite chains, and conversely. We show that every such effect algebra can be densely embedded into a complete effect algebra (its MacNeille completion) and that there exists an order continuous state on it.
References:
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