Theorems · Definition · number theory

IsDecompositionField.ringEquiv

(K : Type u_2) →
  (L : Type u_3) →
    {B : Type u_4} →
      [inst : Field K] →
        [inst_1 : Field L] →
          [inst_2 : Algebra K L] →
            [inst_3 : CommRing B] →
              (P : Ideal B) →
                (D : Type u_5) →
                  [inst_4 : Field D] →
                    [inst_5 : Algebra D L] →
                      [inst_6 : MulSemiringAction Gal(L/K) B] →
                        (D' : Type u_8) →
                          [inst_7 : Field D'] →
                            [inst_8 : Algebra D' L] →
                              [IsDecompositionField K L P D] → [IsDecompositionField K L P D'] → D ≃+* D'

Two decomposition fields are isomorphic.

Defined in

Mathlib.NumberTheory.RamificationInertia.HilbertTheory

Cited by

2 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraCommRingFieldAlgebraMulSemiringActionFieldAlgebraIsDecompositionFieldIsDecompositionField