 Nondegeneracy of the trace form of a number field

ID: nondegeneracy-of-the-trace-form-of-a-number-field

Codex  0 Created 2026-09-24 Updated 2026-09-24

For nonzero

x \in K

, choose

y = x^{- 1}

. Then

B (x, y) = Tr_{K / Q} (1) = [K : Q] \neq = 0,

so the trace form is nondegenerate.

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