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Lattice effect algebras generalize orthomodular lattices as well as MV-algebras. This means that within lattice effect algebras it is possible to model such effects as unsharpness (fuzziness) and/or non-compatibility. The main problem is the existence of a state. There are lattice effect algebras with no state. For this reason we need some conditions that simplify checking the existence of a state. If we know that the center C(E) of an atomic Archimedean lattice effect algebra E (which is again atomic) is a bifull sublattice of E , then we are able to represent E as a subdirect product of lattice effect algebras E i where the top element of each one of E i is an atom of C(E) . In this case it is enough if we find a state at least in one of E i and we are able to extend this state to the whole lattice effect algebra E . In [8] an atomic lattice effect algebra E (in fact, an atomic orthomodular lattice) with atomic center C(E) was constructed, where C(E) is not a bifull sublattice of E . In this paper we show that for atomic lattice effect algebras E (atomic orthomodular lattices) neither completeness (and atomicity) of C(E) nor σ -completeness of E are sufficient conditions for C(E) to be a bifull sublattice of E .

Two Remarks to Bifullness of Centers of Archimedean Atomic Lattice Effect Algebras