On wsq-primary ideals

ASLANKARAYİĞİT UĞURLU E., Bouba E. M., TEKİR Ü., KOÇ S.

Czechoslovak Mathematical Journal, cilt.73, sa.2, ss.415-429, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 73 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.21136/cmj.2023.0259-21
  • Dergi Adı: Czechoslovak Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.415-429
  • Anahtar Kelimeler: 05C25, 13A15, 13A99, 13F30, primary ideal, quasi-primary ideal, strongly quasi-primary ideal, weakly 2-prime ideal, weakly primary ideal
  • Marmara Üniversitesi Adresli: Evet

Özet

We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let R be a commutative ring with a nonzero identity and Q a proper ideal of R. The proper ideal Q is said to be a weakly strongly quasi-primary ideal if whenever 0 ≠ ab ∈ Q for some a, b ∈ R, then a2 ∈ Q or b∈Q. Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional rings over which every proper ideal is wsq-primary. Finally, we study finite union of wsq-primary ideals.