GOLDIE EXTENDING PROPERTY ON THE CLASS OF z-CLOSED SUBMODULES

TERCAN A., YAŞAR R., Yücel C. C.

Bulletin of the Korean Mathematical Society, cilt.59, sa.2, ss.453-468, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.4134/bkms.b210349
  • Dergi Adı: Bulletin of the Korean Mathematical Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.453-468
  • Anahtar Kelimeler: CLS-module, Complement, extending module, Goldie extending module, rational Hull, z-closed
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this article, we define a module M to be Gz-extending if and only if for each z-closed submodule X of M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We investigate structural properties of Gz-extending modules and lo-cate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for Gz-extending modules. We obtain that if a ring is right Gz-extending, then so is its essential overring. Also it is shown that the Gz-extending property is inherited by its rational hull. Furthermore it is provided some applications including matrix rings over a right Gz-extending ring.