Theorems · Theorem · commutative algebra

IsGaloisGroup.smulCommClassQuotient

∀ (G : Type u_1) [inst : Group G] (A : Type u_2) (B : Type u_3) (C : Type u_4) [inst_1 : CommSemiring A]
  [inst_2 : Semiring C] [inst_3 : Algebra A C] [inst_4 : MulSemiringAction G C] (N : Subgroup G)
  [inst_5 : CommSemiring B] [inst_6 : Algebra B C] [FaithfulSMul B C] [inst_8 : N.Normal] [inst_9 : Algebra A B]
  [IsScalarTower A B C] [SMulCommClass G A C] [inst_12 : MulSemiringAction G B] [inst_13 : MulAction (G ⧸ N) B]
  [SMulDistribClass G B C] [IsScalarTower G (G ⧸ N) B], SMulCommClass (G ⧸ N) A B

If G acts on C commuting with A, then the action of G ⧸ N on B commutes with A.

Defined in

Mathlib.RingTheory.IsGaloisGroup.Basic

Cited by

1 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupCommSemiringSemiringAlgebraMulSemiringActionCommSemiringAlgebraFaithfulSMulSubgroup.NormalAlgebraIsScalarTowerSMulCommClassMulSemiringActionMulActionSMulDistribClassIsScalarTower