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http://dx.doi.org/10.4134/BKMS.b150760

A NOTE ON GORENSTEIN PRÜFER 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 Mathematics and Software Science Sichuan Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.5, 2016 , pp. 1447-1455 More about this Journal
Abstract
In this note, we mainly discuss the Gorenstein $Pr{\ddot{u}}fer$ domains. It is shown that a domain is a Gorenstein $Pr{\ddot{u}}fer$ domain if and only if every finitely generated ideal is Gorenstein projective. It is also shown that a domain is a PID (resp., Dedekind domain, $B{\acute{e}}zout$ domain) if and only if it is a Gorenstein $Pr{\ddot{u}}fer$ UFD (resp., Krull domain, GCD domain).
Keywords
Gorenstein $Pr{\ddot{u}}fer$ domain; Gorenstein projective module; coherent ring; UFD; PID;
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