Let R, S be rings with unity and M be a unital (R, S)-bimodule.
In this paper we give a description of homomorphisms and
skew derivations of the formal triangular matrix ring T = Tri(R, M, S(
and apply it to provide a triangular representation of the skew
polynomial ring T [z;θ,d]. Also we introduce some special mappings
on modules which are generalization of ring homomorphisms
and skew derivations. We characterize the ring endomorphisms
of T, when T [z;θ,d] has a triangular representation. These results
are applied to introduce the notion of skew polynomial modules
and present some results and examples concerning this notion.
