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Some Results on Gorenstein Dedekind Domains and Their Factor Rings
Authors:Kui Hu  Fanggui Wang
Institution:1. College of Mathematics and Software Science , Sichuan Normal University , Chengdu , China hukui200418@163.com;3. College of Mathematics and Software Science , Sichuan Normal University , Chengdu , China
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.
Keywords:Gorenstein dedekind domain  Gorenstein projective module  QF-ring
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