Gorenstein Krull domains and their factor rings

Abstract

The concept of Gorenstein Krull domains can be viewed as a Gorenstein analogue of Krull domains, which are not necessarily integrally closed. This allows us to study those domains from the point view of Gorenstein homological algebra. By the so-called w-operation, we prove that an integral domain is Gorenstein Krull if and only if for any nonzero nonunit, the Gorenstein global dimension of its w-factor ring is zero.

KEYWORDS:

• G-Krull domain
• QF-ring
• SM-domain
• w-factor ring

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13F05
• 13G05;13D05

Acknowledgments

This work is supported by Scientific Research Foundation of Chengdu University of Information Technology (KYTZ202015, KYTD202331).