Σ-Extending Modules, Σ-Lifting Modules, and Proper Classes

Abstract

We introduce generalizations of extending modules and lifting modules relative to proper classes of short exact sequences of modules, and we characterize modules for which any direct sums of copies of them are such relative extending modules or relative lifting modules.

Key Words:

• Extending module
• Lifting module
• Precover
• Preenvelope
• Proper class

2000 Mathematics Subject Classification:

• 16D80

ACKNOWLEDGMENTS

The author thanks Lidia Angeleri Hügel for helpful and inspiring discussions on the question if the class PAdd(ℳ) is covering.

The author acknowledges the support of the grants CEEX-ET 47/2006 and CNCSIS-AT 72/2006.

Notes

Communicated by J. L. Gómez Pardo.