Strongly Max-Flat Modules

Abstract

Let R be a ring. A left R-module M is called strongly max-flat if for every simple right R-module S and every i ≥ 1. In this article, we show that the class of strongly max-flat R-modules and its Ext-orthogonal class form a perfect and hereditary cotorsion pair. This result has some applications to the characterizations of right SF, semisimple, left perfect, von Neumann regular and quasi-Frobenius rings.

Key Words:

• Generalized Noetherian ring
• Strongly max-cotorsion module
• Strongly max-flat module

2010 Mathematics Subject Classification:

• 16D40
• 16E10
• 16E30

ACKNOWLEDGMENTS

This research was partially supported by National Natural Science Foundation of China (No. 11071111). I would like to express my gratitude to my advisor Professor Ding Nanqing for his constant encouragement and guidance. I also thank the referee for his or her valuable suggestions and comments.

Notes

Communicated by T. Albu.