IJPAM: Volume 25, No. 3 (2005)


Moharram A. Khan
Department of Mathematics
Eritrea Institute of Technology
Mai-Nefhi, P.O. Box 10373, Asmara, ERITREA
e-mail: moharram_a@yahoo.com

Abstract.In the present paper, we first establish, in Section 2, some decomposition theorems for rings and its subsets (see Theorem 2.1 and Theorem 2.2, for details). Secondly, in Section 3, certain nearrings satisfying one of the defined properties $(C)$ to $(C_{5})$, under appropriate conditions such nearrings are in fact shown to be commutative. Thirdly, in Section 4, it is proved that any nearring is decomposable into a direct sum of special sub nearrings and the Pierce-decomposition for rings is generalized. Finally, in Section 5, we provide some counterexamples which show that hypotheses of our theorems are not altogether superfluous.

Received: August 22, 2005

AMS Subject Classification: 16Y30, 16U80

Key Words and Phrases: decomposition theorem, $J$-ring, nil ring, periodic nearring, zero-commutative, distributively-generated $(d-g)$ nearing, $D$-nearring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 3