TRIANGULAR MATRIX REPRESENTATIONS OF SKEW MONOID RINGS

Let R be a ring and S a u.p.-monoid. Assume that there is a monoid homomorphism α : S → Aut (R). Suppose that α is weakly　rigid and l_R(Ra) is pure as a left ideal of R for every element a ∈ R. Then the skew monoid ring R*S induced by α has the same triangulating dimension as R. Furthermore, if R is a PWP ring, then so is R*S.