Abstract
The well-known fundamental identity in number theory expresses the degree of an extension of global fields in terms of local information. In this article we show a generalized fundamental identity for arbitrary Dedekind domains. As an application, we show that any Japanese Dedekind domain is excellent.
Funding Statement
The author is partially support by the MoST grant 109-2115-M-001-002-MY3.
Acknowledgments
The author thanks Raymond Heitmann who kindly informed him an example of a locally Nagata principal ideal domain which is not Nagata [10]. He also thanks the referee for a careful reading and the reference [13].
Citation
Chia-Fu Yu. "Japanese Dedekind Domains Are Excellent." Taiwanese J. Math. 26 (3) 483 - 500, June, 2022. https://doi.org/10.11650/tjm/220102
Information
