Japanese Dedekind domains are excellent

TL;DR

This paper generalizes a fundamental identity in number theory to arbitrary Dedekind domains and proves that Japanese Dedekind domains possess the property of being excellent, extending their known algebraic qualities.

Contribution

It introduces a generalized fundamental identity for Dedekind domains and establishes that Japanese Dedekind domains are inherently excellent, broadening understanding of their algebraic structure.

Findings

Generalized fundamental identity for Dedekind domains

Japanese Dedekind domains are proven to be excellent

Extension of classical number theory results

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 already excellent.