spectralAlgNorm_extends — Mathlib

English

There is a SeminormClass instance for the AlgebraNorm on the normalClosure inside AlgebraicClosure, compatible with the ambient field operations.

Русский

Существует экземпляр SeminormClass на AlgebraNorm над normalClosure внутри AlgebraicClosure, совместимый с операциями поля.

LaTeX

$$$\text{SeminormClass}(\text{AlgebraNorm } K \text{ (normalClosure } K(E)\,\text{ (AlgebraicClosure } E)))$$$

Lean4

theorem spectralAlgNorm_extends (k : K) : spectralAlgNorm K L (algebraMap K L k) = ‖k‖ :=
  spectralNorm_extends k

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