Theorems · Definition · commutative algebra

Ideal.Quotient.stabilizerHom

{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] →
                      [SMulCommClass G A B] → ↥(MulAction.stabilizer G P) →* (B ⧸ P) ≃ₐ[A ⧸ p] B ⧸ P

If P lies over p, then the stabilizer of P acts on the extension (B ⧸ P) / (A ⧸ p).

Defined in

Mathlib.RingTheory.Ideal.Over

Cited by

10 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraIdeal.LiesOverGroupMulSemiringActionSMulCommClass