IJPAM: Volume 87, No. 6 (2013)

ON STRONG IFP NEAR-RINGS

P. Dheena$^1$, B. Elavarasan$^2$
$^1$Department of Mathematics
Annamalai University
Annamalainagar, 608 002, INDIA
$^2$Department of Mathematics
Karunya University
Coimbatore, 641 114, Tamilnadu, INDIA


Abstract. In this paper, we introduce the notion of strong IFP and weak IFP near-rings. Weak IFP near-ring is a generalization of IFP near-ring. We study the basic properties of right weak IFP near-rings. We show that if $N$ is a 2-primal near-ring and if $N$ is strong IFP, then $N$ is left weakly regular if and only if every prime ideal of $N$ is maximal.

Received: September 6, 2013

AMS Subject Classification: 16Y30

Key Words and Phrases: regular, IFP near-ring, reduced, 2-primal and weakly regular

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DOI: 10.12732/ijpam.v87i6.9 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: 2013
Volume: 87
Issue: 6