IJPAM: Volume 91, No. 1 (2014)


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

Abstract. For a monoid $M$, we introduce nil 3-$M$-Armendariz, which are a common generalization of nil 3-Armendariz and 3-$M$-Armendariz rings, and investigates their properties. We show that a ring $R$ is nil 3-$M$-Armendariz ring if and only if for any $n\in \mathbb{N}, T_{n}(R)$ is nil 3-$M$-Armendariz, where $M$ is a monoid. Also we show that if a ring $R$ is semicommutative which is also nil 3-$M$-Armendariz, then $R$ is nil 3-$(M \times N)$-Armendariz, where $N$ is a unique product monoid.

Received: November 30, 2013

AMS Subject Classification: 16S36, 16U20, 16N60, 16U99

Key Words and Phrases: unique product monoid, 3-Armendariz ring, nil 3-Armendariz ring, 3-$M$-Armendariz ring, nil 3-$M$-Armendariz

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DOI: 10.12732/ijpam.v91i1.10 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 91
Issue: 1