On Covers and Envelopes under Hom and Tensor Functors

Abstract

Let R be a commutative ring. We investigate the relationship between (pre)covers ((pre)envelopes) of an R-module and the counterparts of the corresponding homomorphism module or tensor product module. Some applications are also given.

Key Words:

• Homomorphism module
• (Pre)cover
• (Pre)envelope
• Reflexive module
• Tensor product module

2010 Mathematics Subject Classification:

• 16D90
• 18G25

ACKNOWLEDGMENTS

The authors would like to thank the referee for many helpful comments and suggestions.

Notes

Communicated by T. Albu.