Theorems · Theorem · ring theory
Ideal.isHopfIdeal_iff
∀ (R : Type u_1) {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : HopfAlgebraStruct R A] (I : Ideal A),
Ideal.IsHopfIdeal R I ↔
(Submodule.restrictScalars R I).IsCoideal ∧ ∀ ⦃x : A⦄, x ∈ I → (HopfAlgebraStruct.antipode R) x ∈ I- Defined in
- Mathlib.RingTheory.HopfAlgebra.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Submodule.restrictScalarsstatement and proof · cited by 180
- HopfAlgebraStruct.antipodestatement and proof · cited by 38
- Submodule.IsCoidealstatement and proof · cited by 17
- HopfAlgebraStructstatement and proof · cited by 6
- Ideal.IsHopfIdealstatement and proof · cited by 4
- Ideal.IsHopfIdeal.casesOnproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.