Theorems · Theorem · commutative algebra
FractionalIdeal.isPrincipal.of_isPrincipal_pow_of_coprime
∀ {R : Type u_1} {K : Type u_2} [inst : CommRing R] [inst_1 : Field K] [inst_2 : Algebra R K] [IsFractionRing R K]
[inst_4 : IsDomain R] [IsDedekindDomain R] [inst_6 : Fintype (ClassGroup R)] {n : ℕ},
n.Coprime (Fintype.card (ClassGroup R)) →
∀ (I : FractionalIdeal (nonZeroDivisors R) K), (↑(I ^ n)).IsPrincipal → (↑I).IsPrincipalA fractional ideal is principal if a power coprime to the class number is principal.
- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Unitsproof · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- Units.valproof · cited by 1,966
- Fintype.cardstatement and proof · cited by 1,386
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.