2021•Iraqi Journal of ScienceOpen access

N Sequence Prime Ideals

Hemin A. Ahmad, Parween A. Hummadi

Abstract

In this paper, the concepts of -sequence prime ideal and -sequence quasi prime ideal are introduced. Some properties of such ideals are investigated. The relations between -sequence prime ideal and each of primary ideal, -prime ideal, quasi prime ideal, strongly irreducible ideal, and closed ideal, are studied. Also, the ideals of a principal ideal domain are classified into quasi prime ideals and -sequence quasi prime ideals.

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Key concepts: Ideal (ethics), Prime (order theory), Prime ideal, Boolean prime ideal theorem, Prime element, Mathematics, Sequence (biology), Associated prime