Some remarks on strongly irreducible ideals

Authors

  • Jamal Hashemi zadeh Dezfuly Shahid Chamran University of Ahvaz, Iran
  • Fatemeh Hassanzadeh

DOI:

https://doi.org/10.30495/jme.v18i0.3134

Keywords:

Arithmetical ring, duo ring, Goldie type ring, quasi regular, strongly irreducible ideal, strongly zero divisor

Abstract

A proper ideal I of a ring R is called strongly irreducible ideal (briefly, SI-ideal) whenever I contains the intersection of two ideals of R, I contains at least one of
those ideals. It is clear that any prime ideal is a strongly irreducible ideal. Therefore, these ideals can be considered generalizations of the prime ideals. From this point of view, in this paper we extend some results of prime ideals to SI-ideals. As an example, we show that the number of minimal SI-ideals in noetherian arithmetical rings is finite and in these rings every ideal contains a finite intersection of SI-ideals. Also we give a similar result of the prime avoidance lemma for SI-ideals.

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Published

2024-10-28

Issue

Vol. 18

Section

Vol. 18, No. 6, (2024)

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