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Keywords:
effect algebra; orthomodular poset; state; rank of a matrix
effect algebra; orthomodular poset; state; rank of a matrix
Summary:
In the matrix representation of an effect algebra $L$ (in particular, an orthomodular poset), if $L$ admits a state, then its matrix $M(L)$ has the augmentation property ($\text{rank}(M(L)) = \text{rank}(M(L)|1)$). We show that the reverse implication is not true, thus answering an open question published on effect algebras.
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