IJPAM: Volume 95, No. 4 (2014)

STRONGLY SEMICOMMUTATIVE RINGS
RELATIVE TO A MONOID

Ayoub Elshokry$^1$, Eltiyeb Ali$^{2}$
$^{1,2}$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 strongly semicommutative rings relative to $M$, which are a generalization of strongly semicommutative rings, and investigates its properties. We show that every reduced ring is strongly $M$-semicommutative for any unique product monoid $M.$ Also it is shown that for a monoid $M$ and an ideal $I$ of $R.$ If $I$ is a reduced ring and $R/I$ is strongly $M$-semicommutative, then $R$ is strongly $M$-semicommutative.

Received: June 30, 2014

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

Key Words and Phrases: unique product monoid, reduced rings, semicommutative rings, strongly semicommutative rings, strongly semicommutative rings relative to $M$

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DOI: 10.12732/ijpam.v95i4.14 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: 95
Issue: 4
Pages: 611 - 622


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