GOLDIE EXTENDING PROPERTY ON THE CLASS OF z-CLOSED SUBMODULES
Bulletin of the Korean Mathematical Society, cilt.59, sa.2, ss.453-468, 2022 (SCI-Expanded, Scopus)
- 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.