  The aim of our paper is twofold. First, we thoroughly study the set of meager
elements M(E), the center C(E) and the compatibility center B(E)in the setting
of atomic Archimedean lattice effect algebras E. The main result is that in
this case the center C(E) is bifull (atomic) iff the compatibility center B(E)
is bifull (atomic) whenever E is sharply dominating. As a by-product, we give a
new descriciption of the smallest sharp element over x in E via the basic
decomposition of x. Second, we prove the Triple Representation Theorem for
sharply dominating atomic Archimedean lattice effect algebras.
