ON NILPOTENT POWER SERIES WITH NILPOTENT COEFFICIENTS

Abstract

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem ex- tended the nil-Armendariz property for polynomial rings onto power- series rings, say nil power-serieswise rings. In this paper, we intro- duce the notion of power-serieswise CN rings that is a generalization of nil power-serieswise Armendariz rings. Finally, we study the nil- Armendariz property for Ore extensions and skew power series rings.