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Theorems · Definition · number theory

NumberField.RingOfIntegers.equiv

{K : Type u_1} →
  [inst : Field K] →
    (R : Type u_3) →
      [inst_1 : CommRing R] → [inst_2 : Algebra R K] → [IsIntegralClosure R ℤ K] → NumberField.RingOfIntegers K ≃+* R

The ring of integers of K are equivalent to any integral closure of ℤ in K

Defined in
Mathlib.NumberTheory.NumberField.Basic
Cited by
0 results in Mathlib
Foundations
Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldCommRingAlgebraIsIntegralClosure
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Around this declaration

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

Rat.IsIntegralClosure.intEquiv · cited by 6IsIntegralClosure.intEquivRat.ringOfIntegersEquiv · cited by 6Rat.ringOfIntegersEquivNumberField.RingOfIntegers.withValEquiv · cited by 2RingOfIntegers.withValEqu…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraField · cited by 7404FieldRingEquiv · cited by 1147RingEquivAlgEquiv.symm · cited by 615AlgEquiv.symmNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersIsIntegralClosure · cited by 146IsIntegralClosureAlgEquiv.toRingEquiv · cited by 137AlgEquiv.toRingEquivIsIntegralClosure.equiv · cited by 11IsIntegralClosure.equivRingOfIntegers.equivCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.