ON OVERRINGS OF GORENSTEIN DEDEKIND DOMAINS

Title & Authors
ON OVERRINGS OF GORENSTEIN DEDEKIND DOMAINS
Hu, Kui; Wang, Fanggui; Xu, Longyu; Zhao, Songquan;

Abstract
In this paper, we mainly discuss Gorenstein Dedekind do-mains (G-Dedekind domains for short) and their overrings. Let R be a one-dimensional Noetherian domain with quotient field K and integral closure T. Then it is proved that R is a G-Dedekind domain if and only if for any prime ideal P of R which contains ($\small{R\;:_K\;T}$), P is Gorenstein projective. We also give not only an example to show that G-Dedekind domains are not necessarily Noetherian Warfield domains, but also a definition for a special kind of domain: a 2-DVR. As an application, we prove that a Noetherian domain R is a Warfield domain if and only if for any maximal ideal M of R, $\small{R_M}$ is a 2-DVR.
Keywords
Gorenstein projective module;Gorenstein Dedekind domain;strongly Gorenstein projective module;n-strongly Gorenstein projective module;Noetherian Warfield domain;2-DVR;
Language
English
Cited by
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