Korean J. Math. Vol. 21 No. 1 (2013) pp.41-53
DOI: https://doi.org/10.11568/kjm.2013.21.1.41

ON NILPOTENT POWER SERIES WITH NILPOTENT COEFFICIENTS

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Tai Keun Kwak
Yang Lee

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.



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