Theorems · Theorem · commutative algebra
IsDedekindDomain.idealFactorsEquivOfQuotEquiv_symm
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : IsDedekindDomain A] {I : Ideal R}
{J : Ideal A} [inst_3 : IsDedekindDomain R] (f : R ⧸ I ≃+* A ⧸ J),
(IsDedekindDomain.idealFactorsEquivOfQuotEquiv f).symm = IsDedekindDomain.idealFactorsEquivOfQuotEquiv f.symm- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, 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.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Set.Elemstatement · cited by 7,166
- Set.ofPredstatement · cited by 6,101
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- RingEquivstatement and proof · cited by 1,147
- OrderIsostatement · cited by 874
- IsDedekindDomainstatement and proof · cited by 668
- RingEquiv.symmstatement · cited by 567
- OrderIso.symmstatement · cited by 475
- IsDedekindDomain.idealFactorsEquivOfQuotEquivstatement · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- idealFactorsEquivOfQuotEquiv_symmproof · cited by 0