The Armendariz module and its application to the Ikeda-Nakayama module

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+⋯+am...

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Main Author: M. Tamer Koşan
Format: Article
Language:English
Published: Wiley 2006-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/IJMMS/2006/35238
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author M. Tamer Koşan
author_facet M. Tamer Koşan
author_sort M. Tamer Koşan
collection DOAJ
description 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.
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spelling doaj-art-e372ab6dba274676b770c95981f01a682025-02-03T06:00:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/3523835238The Armendariz module and its application to the Ikeda-Nakayama moduleM. Tamer Koşan0Department of Mathematic, Faculty of Science-Literature, Kocatepe University, ANS Campus, Afyon 03200, TurkeyA 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.http://dx.doi.org/10.1155/IJMMS/2006/35238
spellingShingle M. Tamer Koşan
The Armendariz module and its application to the Ikeda-Nakayama module
International Journal of Mathematics and Mathematical Sciences
title The Armendariz module and its application to the Ikeda-Nakayama module
title_full The Armendariz module and its application to the Ikeda-Nakayama module
title_fullStr The Armendariz module and its application to the Ikeda-Nakayama module
title_full_unstemmed The Armendariz module and its application to the Ikeda-Nakayama module
title_short The Armendariz module and its application to the Ikeda-Nakayama module
title_sort armendariz module and its application to the ikeda nakayama module
url http://dx.doi.org/10.1155/IJMMS/2006/35238
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