Lifting Property of Direct Sums of Hollow Modules

Abstract

We give necessary and sufficient conditions for a module M with a decomposition that complements maximal direct summands to be a lifting module. We apply our results to get a necessary and sufficient condition for a direct sum of modules to be a quasi-discrete (discrete) module. We also give some sufficient conditions for a lifting module to be a direct sum of indecomposables.

Key Words:

• Complements maximal direct summands
• Direct sums
• Discrete modules
• Lifting modules
• Locally semi T-nilpotent
• Self-projective
• Quasi-discrete modules

2000 Mathematics Subject Classification:

• 16D40

Notes

Communicated by R. Wisbauer.