Some examples in Gorenstein multiplicative ideal theory

Abstract

In this paper, we construct some non-integrally closed domains in Gorenstein multiplicative ideal theory. For example, we show that there exists a Gorenstein Prüfer domain which is neither Gorenstein Dedekind nor Prüfer, and there exists a Gorenstein Krull domain which is neither Gorenstein Dedekind nor Krull. Also, we construct a non-integrally closed non-coherent domain in which all Gorenstein projective (resp., injective, flat) modules are projective (resp., injective, flat).

Keywords:

• G-Dedekind domain
• G-Krull domain
• Gorenstein homological algebra
• G-Prüer domain
• star-operations

2020 Mathematics Subject Classification:

• 13D05
• 13G05
• 13F05

Acknowledgments

The author would like to thank the referee for comments and corrections, which have improved this article.

Additional information

Funding

This work is supported by the Scientific Research Foundation of Chengdu University of Information Technology (No. KYTZ202015).