IJPAM: Volume 85, No. 3 (2013)

P-REGULAR NEARRINGS CHARACTERIZED
BY THEIR BI-IDEALS

Aphisit Muangma1, Aiyared Iampan2
1,2Department of Mathematics
School of Science
University of Phayao
Phayao, 56000, THAILAND


Abstract. Using the idea of quasi-ideals of P-regular nearrings, the concept of bi-ideals of P-regular nearrings is generalized, which is an extension of the concept of quasi-ideals of P-regular nearrings and some interesting characterizations of bi-ideals are obtained. As a result, we prove that every element of a bi-ideal B of a P-regular nearring can be represented as the sum of two elements of P and Q. Moreover, every element of the finite intersection ∩i=1nBi of bi-ideals of a P-regular distributive nearring N can be represented as the sum of two elements of P and B1NB2N ... NBn-1NBn.

Received: December 21, 2012

AMS Subject Classification: 16Y30, 16D25

Key Words and Phrases: $P$-regular nearring, quasi-ideal, bi-ideal

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DOI: 10.12732/ijpam.v85i3.4 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: 85
Issue: 3