Theorems · Theorem · commutative algebra

Ideal.Quotient.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.IsMaximal] [Q.IsMaximal] [SMulCommClass G A B] [Algebra.IsSeparable (A ⧸ P) (B ⧸ Q)],
  Module.Finite (A ⧸ P) (B ⧸ Q)

If the extension B/Q over A/P is separable, then it is finite dimensional.

Defined in

Mathlib.RingTheory.Invariant.Galois

Cited by

0 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFiniteGroupMulSemiringActionAlgebra.IsInvariantIdeal.LiesOverIdeal.IsMaximalIdeal.IsMaximalSMulCommClassAlgebra.IsSeparable