Infinite direct sums of lifting modules

Er N. F.

COMMUNICATIONS IN ALGEBRA, cilt.34, sa.5, ss.1909-1920, 2006 (SCI-Expanded) identifier identifier

  • 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
  • Yıldız Teknik 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.