Triangulating dimension of skew generalized power series rings

Abstract

Let [Formula: see text] be a ring, [Formula: see text] a strictly ordered monoid and [Formula: see text] a monoid homomorphism. In this paper, we investigate the problem when a skew generalized power series ring [Formula: see text] has the same triangulating dimension as the ring [Formula: see text]. 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.