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Theorems · Definition · number theory

NumberField.InfinitePlace.IsRamified

(k : Type u_1) →
  [inst : Field k] → {K : Type u_2} → [inst_1 : Field K] → [Algebra k K] → NumberField.InfinitePlace K → Prop

An infinite place is ramified in a field extension if it is not unramified.

Defined in
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification
Cited by
18 results in Mathlib
Foundations
Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.InfinitePlace.ramifiedPlacesOver · cited by 12InfinitePlace.ramifiedPla…NumberField.InfinitePlace.isRamified_iff · cited by 9InfinitePlace.isRamified_…NumberField.InfinitePlace.IsRamified.finrank_eq_two · cited by 3IsRamified.finrank_eq_twoNumberField.InfinitePlace.IsRamified.isComplex · cited by 3IsRamified.isComplexNumberField.InfinitePlace.IsRamified.isReal · cited by 3IsRamified.isRealNumberField.InfinitePlace.IsRamified.comap_embedding_conjugate · cited by 2IsRamified.comap_embeddin…NumberField.InfinitePlace.IsRamified.isMixed_conjugate_embedding · cited by 2IsRamified.isMixed_conjug…NumberField.InfinitePlace.IsRamified.isMixed_embedding · cited by 2IsRamified.isMixed_embedd…NumberField.InfinitePlace.exists_isConj_of_isRamified · cited by 1InfinitePlace.exists_isCo…NumberField.InfinitePlace.IsRamified.comap_embedding · cited by 1IsRamified.comap_embeddingNumberField.ComplexEmbedding.IsMixed.mk_isRamified · cited by 1IsMixed.mk_isRamifiedNumberField.InfinitePlace.IsRamified.ne_conjugate · cited by 1IsRamified.ne_conjugateNumberField.InfinitePlace.isRamified_iff_card_stabilizer_eq_two · cited by 1InfinitePlace.isRamified_…NumberField.InfinitePlace.isRamified_mk_iff_isMixed · cited by 1InfinitePlace.isRamified_…NumberField.InfinitePlace.union_ramifiedPlacesOver_unramifiedPlacesOver · cited by 1InfinitePlace.union_ramif…Algebra · cited by 11388AlgebraField · cited by 7404FieldNumberField.InfinitePlace · cited by 604NumberField.InfinitePlaceNumberField.InfinitePlace.IsUnramified · cited by 35InfinitePlace.IsUnramifiedInfinitePlace.IsRamifiedCITED BYCITES

Cites4

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Cited by19

Results whose statement or proof uses this declaration.