Skew polynomial rings of formal triangular matrix rings

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 , 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.