Infinite direct sums of lifting modules


Er N. F.

COMMUNICATIONS IN ALGEBRA, vol.34, no.5, pp.1909-1920, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 5
  • Publication Date: 2006
  • Doi Number: 10.1080/00927870500542903
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1909-1920

Abstract

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.