Some Results on Gorenstein Dedekind Domains and Their Factor Rings

Abstract

A domain is called a Gorenstein Dedekind domain (G-Dedekind for short) if every submodule of a projective module is G-projective (i.e., G-gldim(R) = 1). It is proved in this note that a domain R is a G-Dedekind domain if and only if every ideal of R is Gorenstein-projective (G-projective for short). We also show that nontrivial factor rings of Dedekind domains are QF-rings. We also give an example to show that factor rings of QF-rings are not necessarily QF-rings.

Key Words:

• Gorenstein dedekind domain
• Gorenstein projective module
• QF-ring

2000 Mathematics Subject Classification:

• 13G05
• 13D03

ACKNOWLEDGMENTS

The authors are supported by the National Natural Science Foundation of China (11171240). The authors are also grateful to the referee for the valuable comments and suggestions.

Notes

Communicated by E. Kirkman.