  Starting from involutive BE algebras, we redefine the orthomodular algebras,
by introducing the notion of implicative-orthomodular algebras. We investigate
properties of implicative-orthomodular algebras, and give characterizations of
these algebras. Then we define and study the notions of filters and deductive
systems, and characterize certain classes of filters. Furthermore, we introduce
and characterize the commutative deductive systems in implicative-orthomodular
algebras. We also show that any deductive system determines a congruence, and
conversely, for any congruence we can define a deductive system in an
implicative-orthomodular algebra. We define the quotient
implicative-orthomodular algebra with respect to the congruence induced by a
deductive system, and prove that a deductive system is commutative if and only
if all deductive systems of the corresponding quotient algebra are commutative.
