Abstract
We prove that if there exists an order-continuous, faithful valuation ω on a lattice effect algebra E then E is modular, separable and order-continuous. It is also shown that such an effect algebra E can be supremum and infimum densely embedded into a complete effect algebra E ̂ which is also modular separable and order-continuous, since the valuation ω can be extended to a unique order-continuous faithful valuation ω ̂ on E ̂ .
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