2021•Gazi University Journal of Science Part A Engineering and InnovationOpen access

On Prime Ideals Related to an Ideal in a Commutative Ring

Ortaç Öneş

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.

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Key concepts: Associated prime, Radical of an ideal, Ideal (ethics), Primary ideal, Prime ideal, Mathematics, Minimal ideal, Prime (order theory)