Annihilator Condition on Modules

Mahdou N., KOÇ S., YILDIZ E., TEKİR Ü.

Iranian Journal of Science, cilt.47, sa.5-6, ss.1713-1721, 2023 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 5-6
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s40995-023-01533-4
  • Dergi Adı: Iranian Journal of Science
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.1713-1721
  • Anahtar Kelimeler: Annihilator condition, Mccoy modules, r-submodules, Special r-submodules
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Let R be a commutative ring with 1 ≠ 0 and M a unital R-module. M is said to satisfy Property (A) if for each finitely generated ideal J of R contained in ZR(M) , there exists 0≠m∈M such that Jm=(0). Also M is said to satisfy Property (T) if for each finitely generated submodule N of M contained in T(M), there exists 0≠a∈R such that aN=(0). In this article, we study certain annihilator conditions on modules such as Property (A) and Property (T). In addition to give many properties of modules satisfying Property (A) (Property (T)), we characterize these classes of modules in terms of r-submodules and sr-submodules. Also, we give a method to construct non Noetherian rings in which every ideal satisfies Property (A).