FP-PROJECTIVE DIMENSIONS

ABSTRACT

We define a dimension, called an FP-projective dimension, for modules and rings. It measures how far away a finitely generated module is from being finitely presented, and how far away a ring is from being Noetherian. This dimension has nice properties when the ring in question is coherent. The relations between the FP-projective dimension and other homological dimensions are discussed.

Key Words:

• Coherent ring
• FP-injective module
• FP-projective dimension
• FP-projective module
• Noetherian ring

Mathematical Subject Classification:

• Primary 16E10
• Secondary 18G20

ACKNOWLEDGMENTS

This research was partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20020284009), EYPT and NNSF of China (No. 10331030), and the Nanjing Institute of Technology of China (KXJ04095). The authors would like to thank Professor J. Trlifaj for sending them his 2000 paper and the referee for the helpful comments and suggestions.

Notes

^#Communicated by A. Facchini.