Theorems · Definition · commutative algebra

Ideal.stabilizerEquiv

{M : Type u_1} →
  {R : Type u_3} →
    [inst : Group M] →
      [inst_1 : Semiring R] →
        [inst_2 : MulSemiringAction M R] →
          {N : Type u_4} →
            [inst_3 : Group N] →
              [inst_4 : MulSemiringAction N R] →
                (I : Ideal R) →
                  (e : M ≃* N) →
                    (∀ (m : M) (x : R), e m • x = m • x) → ↥(MulAction.stabilizer M I) ≃* ↥(MulAction.stabilizer N I)

Assume that M and N are isomorphic and act in a compatible way on R, then for any ideal I of R, the stabilizer of I in M is isomorphic to the stabilizer of I in N.

Defined in

Mathlib.RingTheory.Ideal.Pointwise

Cited by

4 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupSemiringMulSemiringActionGroupMulSemiringAction