More on the weakly 2-prime ideals of commutative rings

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Issoual M., Mahdou N., TEKİR Ü., KOÇ S.

Filomat, cilt.38, sa.17, ss.6099-6108, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 17
  • Basım Tarihi: 2024
  • Doi Numarası: 10.2298/fil2417099i
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.6099-6108
  • Anahtar Kelimeler: 2-prime ideals, primary ideals, prime ideals, semi-primary ideals, weakly 2-prime ideals
  • Marmara Üniversitesi Adresli: Evet

Özet

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.