Relative Flatness, Mittag–Leffler Modules, and Endocoherence

Abstract

Let M _R be a right R-module over a ring R with S = End(M _R ). We study the coherence of the left S-module _S M relative to a hereditary torsion theory for the category of right R-modules. Various results are developed, many extending known results.

Key Words:

• Preenvelope
• τ-coherent module
• τ-M-flat module
• τ-Mittag–Leffler module

2000 Mathematics Subject Classification:

• 16D40
• 16P70

ACKNOWLEDGMENTS

This research was partially supported by SRFDP (No. 20050284015), NSFC (No. 10331030), NSF of Jiangsu Province of China (No. BK 2005207), and the Nanjing Institute of Technology of China. The authors would like to thank Professor Efim Zelmanov for his suggestions.

Notes

Communicated by E. Zelmanov.