IJPAM: Volume 95, No. 4 (2014)

STRUCTURE OF NEAR-RINGS SATISFYING
CERTAIN POLYNOMIAL IDENTITIES

Abdelkarim Boua$^1$, Ahmed A.M. Kamal$^2$
$^1$Department of Mathematics
Faculty of Sciences of Agadir
Ibn Zohr University
P.O. Box 8106, Agadir, MOROCCO
$^2$Department of Mathematics
Faculty of Sciences
Cairo University, Giza, EGYPT
$^2$King Saud University
College of Science
Department of Mathematics
P.O. Box 2455, Riyadh, 11451, KINGDOM OF SAUDI ARABIA


Abstract. In this paper, we will introduce the concept of two-sided $\alpha$-generalized derivation in prime near-rings as it was outlined by the author N. Argac in [#!N._Argac!#]. Thereafter, we will generalize the same results proved by many authors (see [#!Ashraf!#], [#!Oukhtite!#] and [#!Boua2!#]) in the case of derivations, semiderivations and generalized derivations. Furthermore, we will give examples to demonstrate that the restrictions imposed on the hypothesis of various results are not superfluous.

Received: June 25, 2014

AMS Subject Classification: 16N60, 16W25, 16Y30

Key Words and Phrases: prime near-ring, $(\alpha, 1)$-derivation, $(1, \alpha)$-derivation, two-sided $\alpha$-derivation, two-sided $\alpha$-generalized derivation

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DOI: 10.12732/ijpam.v95i4.13 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: 597 - 610


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