On Prime Ideals Related to an Ideal in a Commutative Ring

Abstract

This article focuses on the notion of prime ideal related to an ideal of a commutative ring. Some of its characteristics are studied and the relations between ideals and prime ideals related to these ideals in a commutative ring are examined. Then some useful connections among them are obtained. Both similarities and differences between prime ideals related to an ideal and prime ideals are pointed out. Moreover a direct connection between prime ideals related to an ideal and radical ideals is obtained.