Theorems · Inductive type · number theory

IsDecompositionField

(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] →
              Ideal B → (D : Type u_5) → [inst_4 : Field D] → [Algebra D L] → [MulSemiringAction Gal(L/K) B] → Prop

Let L/K be a Galois extension of fields and let P be a prime ideal of B. The predicate that says that D is the decomposition field of P in L/K, that is the subfield fixed by the decomposition subgroup of P, that is the stabilizer of P in Gal(L/K).

Defined in

Mathlib.NumberTheory.RamificationInertia.HilbertTheory

Cited by

12 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Quot.sound

Assumes

FieldFieldAlgebraCommRingFieldAlgebraMulSemiringAction