Abstract
We generalize David Foulis’s concept of a compression base on a unital group to effect algebras. We first show that the compressions of a compressible effect algebra form a compression basis and that a sequential effect algebra possesses a natural maximal compression basis. It is then shown that many of the results concerning compressible effect algebras hold for arbitrary effect algebras by focusing on a specific compression base. For example, the foci (or projections) of a compression base form an orthomodular poset. Moreover, one can give a natural definition for the commutant of a projection in a compression base and results concerning order and compatibility of projections can be generalized. Finally it is shown that if a compression base has the projection-cover property, then the projections of the base form an orthomodular lattice.
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