More onthe weakly 2-prime ideals of commutative rings

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Issoual ., Mahdou N., Tekir Ü., Koç S.

FILOMAT, vol.38, no.17, pp.6099-6108, 2024 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 38 Issue: 17
  • Publication Date: 2024
  • Doi Number: 10.2298/fil2417099i
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.6099-6108
  • Marmara University Affiliated: Yes

Abstract

 Let R be a commutative ring with a nonzero identity. In this paper, we introduce the concept of weakly 2-prime ideal which is a generalization of 2-prime ideal and both are generalizations of prime ideals. A proper ideal I of R is called weakly 2-prime ideal if whenever a,b ∈ R with 0 ab ∈ I, then a2 or b2 lies in I. A number results concerning weakly 2-prime ideals are given. Furthermore, we characterize the valuation domain and the rings over which every weakly 2-prime ideal is 2-prime and rings over which every weakly 2-prime ideal is semi-primary (i.e √ I is a prime ideal). We study the transfer the notion of weakly 2-prime ideal to amalgamted algebras along an ideal A ▷◁f J