N Sequence Prime Ideals

Hemin A.  Ahmad; Parween A.  Hummadi

doi:10.24996/ijs.2021.62.10.25

Authors

Hemin A. Ahmad Mathematics, College of Education, Salahaddin University, Erbil, Iraq https://orcid.org/0000-0002-3095-7781
Parween A. Hummadi Mathematics, College of Education, Salahaddin University, Erbil, Iraq

DOI:

https://doi.org/10.24996/ijs.2021.62.10.25

Keywords:

Prime ascending chain of ideals, Prime with respect to, Length of an ideal, n-sequence prime ideal, n-sequence quasi prime ideal

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.