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

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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ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr