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http://dx.doi.org/10.11568/kjm.2013.21.1.41

ON NILPOTENT POWER SERIES WITH NILPOTENT COEFFICIENTS  

Kwak, Tai Keun (Department of Mathematics Daejin University)
Lee, Yang (Department of Mathematics Pusan National University)
Publication Information
Korean Journal of Mathematics / v.21, no.1, 2013 , pp. 41-53 More about this Journal
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 extended the nil-Armendariz property for polynomial rings onto power-series rings, say nil power-serieswise rings. In this paper, we introduce 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.
Keywords
nil-Armendariz ring property; polynomial ring; von Neumann regular ring; Ore extension;
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