IsUnmixed — Mathlib

English

IsConj φ σ ↔ IsConj φ σ.symm

Русский

IsConj φ σ ↔ IsConj φ σ.symm

LaTeX

$$IsConj φ σ ↔ IsConj φ σ.symm$$

Lean4

/-- If `L/K` and `φ : L →+* ℂ`, then `IsMixed K φ` if `φ` is not mixed in `K`, i.e., `φ` is real
if and only if it's restriction to `K` is.

This is the complex embedding analogue of `InfinitePlace.IsUnramified K w`, where
`w : InfinitePlace L`. In this case there is an isomorphism between unmixed embeddings and
unramified infinite places. -/
abbrev IsUnmixed (φ : L →+* ℂ) :=
  IsReal (φ.comp (algebraMap K L)) → IsReal φ

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