Lattice effect algebras with (o)-continuous faithful valuations
We prove that if there exists an order-continuous, faithful valuation omega 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) over cap which is also modular separable and order-continuous, since the valuation omega can be extended to a unique order-continuous faithful valuation  )over cap> on (E) over cap. (C) 2001 Elsevier Science B.V. All rights reserved.
effect algebra valuation state order continuity macneille completion