The maximality property was introduced in [9] in orthomodular posets as
a common generalization of orthomodular lattices and orthocomplete orthomodular
posets. We show that various conditions used in the theory of e ect
algebras are stronger than the maximality property, clear up the connections
between them and show some consequences of these conditions. In particular,
we prove that a Jauch{Piron e ect algebra with a countable unital set of states
is an orthomodular lattice and that a unital set of Jauch{Piron states on an
e ect algebra with the maximality property is strongly order determining.
