Theorems · Theorem · commutative algebra

Ideal.Quotient.stabilizerHom_surjective

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] (G : Type u_3)
  [inst_3 : Group G] [Finite G] [inst_5 : MulSemiringAction G B] [inst_6 : SMulCommClass G A B] (P : Ideal A)
  (Q : Ideal B) [Q.IsPrime] [inst_8 : Q.LiesOver P] [Algebra.IsInvariant A B G],
  Function.Surjective ⇑(Ideal.Quotient.stabilizerHom Q P G)

The stabilizer subgroup of Q surjects onto Aut((B/Q)/(A/P)).

Defined in

Mathlib.RingTheory.Invariant.Basic

Cited by

1 results in Mathlib

Foundations

Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraGroupFiniteMulSemiringActionSMulCommClassIdeal.IsPrimeIdeal.LiesOverAlgebra.IsInvariant