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June, 2022 Japanese Dedekind Domains Are Excellent
Chia-Fu Yu
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Taiwanese J. Math. 26(3): 483-500 (June, 2022). DOI: 10.11650/tjm/220102


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.


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].


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Chia-Fu Yu. "Japanese Dedekind Domains Are Excellent." Taiwanese J. Math. 26 (3) 483 - 500, June, 2022.


Received: 12 September 2021; Revised: 5 January 2022; Accepted: 16 January 2022; Published: June, 2022
First available in Project Euclid: 15 February 2022

Digital Object Identifier: 10.11650/tjm/220102

Primary: 11S15
Secondary: 12J20 , 13F05

Keywords: excellent Dedekind domains , ramification of extensions , valuations

Rights: Copyright © 2022 The Mathematical Society of the Republic of China


Vol.26 • No. 3 • June, 2022
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