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Bull. Korean Math. Soc. 2016; 53(5): 1447-1455

Online first article August 25, 2016      Printed September 30, 2016

https://doi.org/10.4134/BKMS.b150760

Copyright © The Korean Mathematical Society.

A note on Gorenstein Pr\"ufer domains

Kui Hu, Fanggui Wang, and Longyu Xu

Southwest University of Science and Technology, Sichuan Normal University, Southwest University of Science and Technology

Abstract

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In this note, we mainly discuss the Gorenstein Pr\"ufer domains. It is shown that a domain is a Gorenstein Pr\"ufer 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\'ezout domain) if and only if it is a Gorenstein Pr\"ufer UFD (resp., Krull domain, GCD domain).

Keywords: Gorenstein Pr\"ufer domain, Gorenstein projective module, coherent ring, UFD, PID

MSC numbers: 13G05, 13D03

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