Atomic effect algebras with compression bases
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Compression base effect algebras were recently introduced by Gudder . They generalize sequential effect algebras  and compressible effect algebras . The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec . The notion of projection-atomicity is introduced and studied and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.
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