IJPAM: Volume 90, No. 4 (2014)

ON THE EXTENSION OF ARMENDARIZ RINGS
RELATIVE TO A MONOID

Ayoub Elshokry$^1$, Eltiyeb Ali$^2$, Liu Zhong-Kui$^3$
$^{1,2,3}$Department of Mathematics
Northwest Normal University
Lanzhou, 730070, P.R. CHINA
$^{1,2}$Department of Mathematics
Khartoum University
Omdurman, SUDAN


Abstract. For a monoid $M$, we introduce the concept of 3-$M$-Armendariz rings, which is a generalization of $M$-Armendariz rings, and investigate its properties. The results prove that the subrings of 3-$M$-Armendariz rings are 3-$M$-Armendariz rings. Every ring satisfying condition $(P)$ is 3-$M$-Armendariz for any unique product monoid $M$. If a ring $R$ is 3-$M$-Armendariz and satisfies condition $(P)$, then $S_{3}(R)$ is 3-$M$-Armendariz. Sufficient and necessary conditions are given for a ring $R$ to be 3-$M$-Armendariz.

Received: October 30, 2013

AMS Subject Classification: 16U20, 16N60, 16U99

Key Words and Phrases: Armendariz ring, 3-Armendariz ring, 3-$M$-Armendariz ring

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DOI: 10.12732/ijpam.v90i4.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 90
Issue: 4