A homological characterization of Krull domains II

Abstract

In this article, we introduce a new type of projective modules, called the weak w-projective module. By using this type of modules, we give a homological characterization of Krull domains. More precisely, it is shown that an integral domain is a Krull domain if and only if every submodule of a projective module is weak w-projective.

Keywords:

• Krull domain
• strong w-module
• weak w-projective module
• weak w-projective dimension
• global weak w-projective dimension

2010 Mathematics Subject Classification:

• 13F05
• 13D07
• 13D05
• 13D30

Acknowledgements

The authors would like to thank the referee for suggestions that resulted in several significant improvements. This work was partially supported by NSFC (Nos. 11671283 and 11701398), NSFC (Tianyuan Fund for Mathematics, No. 11626162), the Scientific Research Fund of Sichuan Normal University (No. 16QP02), and the Scientific Research Fund of Sichuan Provincial Education Department (No. 17ZB0362).

Disclosure statement

No potential conflict of interest was reported by the authors.