(untitled) (European Journal of Pure and Applied Mathematics, 2018)
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 many other rings such as local ring and semisimple NI-ring. Also, we show the following result concerned, the ring of skew Hurwitz series.Â If R is a weak right PS-ring, then the ring of skew Hurwitz seriesÂ is a weak right PS-ring.