Theorems · Theorem · commutative algebra
Ideal.inertiaEquiv_symm_apply_smul
∀ {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)
(he : ∀ (m : M) (x : R), e m • x = m • x) (n : ↥(Ideal.inertia N I)) (x : R), (I.inertiaEquiv e he).symm n • x = n • x- Defined in
- Mathlib.RingTheory.Ideal.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Groupstatement and proof · cited by 6,238
- Idealstatement and proof · cited by 4,748
- Subgroupstatement · cited by 3,593
- MulEquivstatement and proof · cited by 1,142
- MulEquiv.symmstatement and proof · cited by 482
- MulSemiringActionstatement and proof · cited by 423
- MulEquiv.apply_symm_applyproof · cited by 37
- Ideal.inertiastatement and proof · cited by 21
- Ideal.inertiaEquivstatement and proof · cited by 4
- Ideal.inertiaEquiv_apply_smulproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsInertiaField.of_isGaloisGroupproof · cited by 0