IJPAM: Volume 15, No. 1 (2004)


Moharram A. Khan
Department of Mathematics
Eritrea-Institute of Technology
Mai-Nefhi, P.O. Box 1056, Asmara, ERITREA
e-mail: moharram_a@yahoo.com

Abstract.In their paper [3], Ratti et al proved that a semi ring is anti-commutative if and only if it is a product of two semi rings $S_{1}$ and $S_{2}$ such that $S_{1}$ is a left multiplication and $S_{2}$ is a right multiplication. The object of the present paper is to extend the above results for a product of $n$ semi rings $S_{1}$, $S_{2}$,$S_{3}$,$ . . . $, $S_{n}.$ We improve and make extensive use of Ratti and Lin's method throughout. Finally, we provide a counterexample which shows that the hypothesis of our theorems are not all together superfluous.

Received: May 31, 2004

AMS Subject Classification: 16A78, 16Y60

Key Words and Phrases: anti-commutative, idempotent, isomorphism, semi ring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 15
Issue: 1