International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 35238, 7 pages
doi:10.1155/IJMMS/2006/35238
The Armendariz module and its application to the Ikeda-Nakayama
module
Department of Mathematic, Faculty of Science-Literature, Kocatepe University, ANS Campus, Afyon 03200, Turkey
Received 21 December 2005; Revised 5 July 2006; Accepted 5 September 2006
Copyright © 2006 M. Tamer Koşan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
A ring R is called a right Ikeda-Nakayama
(for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if ℓ(I∩J)=ℓ(I)+ℓ(J) for all right ideals I and J of R. R is called Armendariz ring if whenever polynomials f(x)=a0+a1x+⋯+amxm, g(x)=b0+b1x+⋯+bnxn∈R[x] satisfy f(x)g(x)=0, then aibj=0 for each i,j. In this paper, we show that if R[x] is a right IN-ring, then R is a right IN-ring in case R is an Armendariz ring.