Model Structures on Categories of Complexes Over Ding-Chen Rings

Abstract

The so-called Ding–Chen ring is an n-FC ring which is both left and right coherent, and has both left and right self FP-injecitve dimensions at most n for some non-negative integer n. In this article, we introduce the so-called Ding projective, Ding injective complexes, and show that over Ding–Chen rings the homotopy theory on the category of modules can be extended to a homotopy theory on the category of complexes.

Key Words:

• Cotorsion pairs
• Ding-Chen rings
• Ding projective and Ding injective complexes
• Gorenstein flat complexes
• Model structures

2010 Mathematics Subject Classification:

• 18G25
• 18G35
• 55U15
• 55U35

ACKNOWLEDGMENTS

The authors thank the referee for his/her careful reading and many considerable suggestions, which have improved the present article.

This work was partly supported by NSF of China (Grant No. 11101197; 10901129; 10960121).

Notes

Communicated by I. Swanson.