Theorems · Definition · commutative algebra

Ideal.inertiaEquiv

{M : Type u_1} →
  [inst : Group M] →
    {N : Type u_4} →
      [inst_1 : Group N] →
        {R : Type u_5} →
          [inst_2 : Ring R] →
            [inst_3 : MulSemiringAction M R] →
              [inst_4 : MulSemiringAction N R] →
                (I : Ideal R) →
                  (e : M ≃* N) → (∀ (m : M) (x : R), e m • x = m • x) → ↥(Ideal.inertia M I) ≃* ↥(Ideal.inertia 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 inertia subgroup of I in M is isomorphic to the inertia subgroup of I in N.

Defined in

Mathlib.RingTheory.Ideal.Pointwise

Cited by

4 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

GroupGroupRingMulSemiringActionMulSemiringAction