On Skew Triangular Matrix Rings

For a ring R, endomorphism α of R and positive integer n we define a skew triangular matrix ring T n (R, α). By using an ideal theory of a skew triangular matrix ring T n (R, α) we can determine prime, primitive, maximal ideals and radicals of the ring R[x; α]/ ⟨ x n ⟩, for each positive integer n, where R[x; α] is the skew polynomial ring, and ⟨ x n ⟩ is the ideal generated by x n .