Infinite direct sums of lifting modules
COMMUNICATIONS IN ALGEBRA, cilt.34, sa.5, ss.1909-1920, 2006 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 5
- Basım Tarihi: 2006
- Doi Numarası: 10.1080/00927870500542903
- Dergi Adı: COMMUNICATIONS IN ALGEBRA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.1909-1920
- Anahtar Kelimeler: Artinian ring, direct sum, lifting module, noetherian ring, quasi-projective module
- Dokuz Eylül Üniversitesi Adresli: Hayır
Özet
A module M over a ring R is called a lifting module if every submodule A of M contains a direct summand K of M such that A/K is a small submodule of M/K (e.g., local modules are lifting). It is known that a (finite) direct sum of lifting modules need not be lifting. We prove that R is right Noetherian and indecomposable injective right R-modules are hollow if and only if every injective right R-module is a direct sum of lifting modules. We also discuss the case when an infinite direct sum of finitely generated modules containing its radical as a small submodule is lifting.