Theorems · Theorem · commutative algebra

Ideal.Quotient.map_ker_stabilizer_subtype

∀ {A : Type u_3} {B : Type u_4} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B] (P : Ideal B)
  (p : Ideal A) [inst_3 : P.LiesOver p] (G : Type u_6) [inst_4 : Group G] [inst_5 : MulSemiringAction G B]
  [inst_6 : SMulCommClass G A B],
  Subgroup.map (MulAction.stabilizer G P).subtype (Ideal.Quotient.stabilizerHom P p G).ker = Ideal.inertia G P

Defined in

Mathlib.RingTheory.Ideal.Over

Cited by

0 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIdeal.LiesOverGroupMulSemiringActionSMulCommClass