Theorems · Theorem · commutative algebra

IsFractionRing.isInvariant

∀ (G : Type u_1) (A : Type u_2) (B : Type u_3) (K : Type u_4) (L : Type u_5) [inst : Group G] [inst_1 : CommRing A]
  [inst_2 : CommRing B] [inst_3 : Algebra A B] [inst_4 : Field K] [inst_5 : Field L] [inst_6 : Algebra K L]
  [inst_7 : Algebra A K] [inst_8 : Algebra B L] [inst_9 : Algebra A L] [IsFractionRing A K] [IsFractionRing B L]
  [IsScalarTower A K L] [IsScalarTower A B L] [inst_14 : MulSemiringAction G B] [inst_15 : MulSemiringAction G L]
  [SMulDistribClass G B L] [hAB : Algebra.IsInvariant A B G] [SMulCommClass G A B] [Finite G], Algebra.IsInvariant K L G

If G acts on B/A with A as the fixed subring, then G also acts on L/K with K as the fixed subfield, where K and L are the fraction fields of A and B respectively.

Defined in

Mathlib.RingTheory.Invariant.Basic

Cited by

0 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupCommRingCommRingAlgebraFieldFieldAlgebraAlgebraAlgebraAlgebraIsFractionRingIsFractionRingIsScalarTowerIsScalarTowerMulSemiringActionMulSemiringActionSMulDistribClassAlgebra.IsInvariantSMulCommClassFinite