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Near Prime Spectrum

. Hadi. J. Mustafa --- Ameer Mohammad-Husain Hassan

Journal of Kufa for Mathematics and Computer مجلة الكوفة للرياضيات والحاسوب
ISSN: 11712076 Year: 2013 Volume: 1 Issue: 8 Pages: 58-70
Publisher: University of Kufa جامعة الكوفة

Abstract

Let R be a commutative ring with identity . It is well known that a topology was defined for Spec(R)={I:IisaprimeidealofR} called the Zariski topology (prime spectrum) . In this paper we will generalize this idea for near prime ideal . If N be a commutative near-ring with identity ,P_N be a near prime ideal of N and define Spec(N)={P_N:P_N isanearprimeideal } . Then Spec(N) can be endowed with a topology similar to the Zariski topology which is called near Zariski topology (near prime spectrum) .we studies and discuss some of properties of such topology .

Keywords

prime ideal --- near prime ideal --- prime spectrum --- near prime spectrum .