Theorems · Theorem · commutative algebra
Ideal.absNorm_eq_one_iff
∀ {S : Type u_1} [inst : CommRing S] [inst_1 : IsDedekindDomain S] [inst_2 : Module.Free ℤ S] {I : Ideal S},
Ideal.absNorm I = 1 ↔ I = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- Ideal.absNormstatement · cited by 123
- Ideal.absNorm_applyproof · cited by 5
- Submodule.cardQuot_eq_one_iffproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- NumberField.HeightOneSpectrum.one_lt_absNormproof · cited by 3
- RingOfIntegers.exponent_eq_one_iffproof · cited by 2
- RingOfIntegers.isPrincipalIdealRing_of_abs_discr_ltproof · cited by 2
- NumberField.torsionOrder_dvd_absNorm_sub_oneproof · cited by 0