Annihilator Condition on Modules

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

Iranian Journal of Science, vol.47, no.5-6, pp.1713-1721, 2023 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 5-6
  • Publication Date: 2023
  • Doi Number: 10.1007/s40995-023-01533-4
  • Journal Name: Iranian Journal of Science
  • Journal Indexes: Scopus
  • Page Numbers: pp.1713-1721
  • Keywords: Annihilator condition, Mccoy modules, r-submodules, Special r-submodules
  • Marmara University Affiliated: Yes

Abstract

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).