Triangulating dimension of skew generalized power series rings

Let R be a ring, S a strictly ordered monoid and omega : S -> End(R) a monoid homomorphism. In this paper, we investigate the problem when a skew generalized power series ring R[[S, omega]] has the same triangulating dimension as the ring R. Furthermore, for a piecewise prime ring we determine a large class of the skew generalized power series ring which have a generalized triangular matrix representation for which the diagonal rings are prime. Our results extend and unify many existing results.