S-principal ideal multiplication modules


Aslankarayiğit Uğurlu E., Koç S., Tekir Ü.

COMMUNICATIONS IN ALGEBRA, cilt.51, sa.5, ss.1-10, 2023 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 5
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1080/00927872.2022.2164772
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1-10
  • Marmara Üniversitesi Adresli: Evet

Özet

In this paper, we study S-Principal ideal multiplication modules. Let A " role="presentation" >A be a commutative ring with 1≠0, S⊆A" role="presentation" >10,SA a multiplicatively closed set and M " role="presentation" >M an A-module. A submodule N of M is said to be an S-multiple of M if there exist s∈S" role="presentation" >sS and a principal ideal I of A such that sN⊆IM⊆N" role="presentation" >sNIMNM " role="presentation" >M is said to be an S-principal ideal multiplication module if every submodule N " role="presentation" >N of M " role="presentation" >M is an S-multiple of M. Various examples and properties of S-principal ideal multiplication modules are given. We investigate the conditions under which the trivial extension A⋉M" role="presentation" >AM is an S⋉0" role="presentation" >S0-principal ideal ring. Also, we prove Cohen type theorem for S-principal ideal multiplication modules in terms of S-prime submodules.