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http://dx.doi.org/10.4134/JKMS.2013.50.5.991

ON OVERRINGS OF GORENSTEIN DEDEKIND DOMAINS  

Hu, Kui (College of Science Southwest University of Science and Technology)
Wang, Fanggui (College of Mathematics and Software Science Sichuan Normal University)
Xu, Longyu (College of Science Southwest University of Science and Technology)
Zhao, Songquan (College of Science Southwest University of Science and Technology)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 991-1008 More about this Journal
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 ($R\;:_K\;T$), 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, $R_M$ 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;
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