Abstract
The notion of PS-rings is extended to the class of weak PS-rings. We explore the algebraic properties of such class and study its relation with some other rings such as a local ring and a semisimple NI-ring. Also, we show the following result concerning, the ring of skew Hurwitz series, A = (HR, sigma): Let R be a a-compatible NI-ring with nil(R) nilpotent, sigma-(e) = e for every idempotent e is an element of R and R a torsion free as a Z-module. If R is a weak right PS-ring, then A = (HR, sigma) is a weak right PS-ring.