Theorems · Definition · number theory

NumberField.RingOfIntegers.mapAlgEquiv

{k : Type u_3} →
  {K : Type u_4} →
    {L : Type u_5} →
      {E : Type u_6} →
        [inst : Field k] →
          [inst_1 : Field K] →
            [inst_2 : Field L] →
              [inst_3 : Algebra k K] →
                [inst_4 : Algebra k L] →
                  [inst_5 : EquivLike E K L] →
                    [AlgEquivClass E k K L] →
                      E → NumberField.RingOfIntegers K ≃ₐ[NumberField.RingOfIntegers k] NumberField.RingOfIntegers L

The isomorphism of algebras (𝓞 K) ≃ₐ[𝓞 k] (𝓞 L) given by restricting an isomorphism of algebras e : K ≃ₐ[k] L to 𝓞 K.

Defined in

Mathlib.NumberTheory.NumberField.Basic

Cited by

0 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldFieldAlgebraAlgebraEquivLikeAlgEquivClass