Theorems · Inductive type · ring theory
Ideal.IsHopfIdeal
(R : Type u_1) → {A : Type u_2} → [inst : CommRing R] → [inst_1 : Ring A] → [HopfAlgebraStruct R A] → Ideal A → PropAn ideal whose underlying R-submodule is a coideal and which is stable under the
antipode (S(I) ⊆ I). Together with I.IsTwoSided, this makes I a Hopf ideal.
- Defined in
- Mathlib.RingTheory.HopfAlgebra.Quotient
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement · cited by 17,173
- Ringstatement · cited by 7,463
- Idealstatement · cited by 4,748
- HopfAlgebraStructstatement · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.IsHopfIdeal.casesOnstatement and proof · cited by 1
- HopfAlgebra.Quotient.antipode_comp_mkₐstatement and proof · cited by 0
- HopfAlgebra.Quotient.antipode_mkstatement and proof · cited by 0
- Ideal.isHopfIdeal_iffstatement and proof · cited by 0
- Ideal.IsHopfIdeal.antipode_memstatement and proof · cited by 0
- Ideal.IsHopfIdeal.recOnstatement and proof · cited by 0