Theorems · Theorem · commutative algebra

Ideal.IsFractionRing.finite_of_isInvariant

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] (G : Type u_3)
  [Finite G] [inst_4 : Group G] [inst_5 : MulSemiringAction G B] [Algebra.IsInvariant A B G] (P : Ideal A) (Q : Ideal B)
  [inst_7 : Q.LiesOver P] [P.IsPrime] [Q.IsPrime] (K : Type u_4) (L : Type u_5) [inst_10 : Field K] [inst_11 : Field L]
  [inst_12 : Algebra K L] [inst_13 : Algebra (A ⧸ P) K] [IsFractionRing (A ⧸ P) K] [inst_15 : Algebra (B ⧸ Q) L]
  [IsFractionRing (B ⧸ Q) L] [inst_17 : Algebra (A ⧸ P) L] [IsScalarTower (A ⧸ P) (B ⧸ Q) L] [IsScalarTower (A ⧸ P) K L]
  [SMulCommClass G A B] [Algebra.IsSeparable K L], Module.Finite K L

Defined in

Mathlib.RingTheory.Invariant.Galois

Cited by

2 results in Mathlib

Foundations

Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFiniteGroupMulSemiringActionAlgebra.IsInvariantIdeal.LiesOverIdeal.IsPrimeIdeal.IsPrimeFieldFieldAlgebraAlgebraIsFractionRingAlgebraIsFractionRingAlgebraIsScalarTowerIsScalarTowerSMulCommClassAlgebra.IsSeparable