  Recently Yang-Roh-Jun introduced the notion of ordered BCI-algebras as a
generalization of BCI-algebras. They also introduced the notions of
homomorphisms and kernels of ordered BCI-algebras and investigated related
properties. Here we extend their investigation to ordered homomorphisms, i.e.,
order-preserving homomorphisms. To this end, the notions of ordered
homomorphism and kernel of ordered BCI-algebras are first defined. Next,
properties associated with (ordered) subalgebras, (ordered) filters and direct
products of ordered BCI-algebras are addressed.
