Some Results on Gorenstein Dedekind Domains and Their Factor Rings

摘要

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.