Theorems · Definition · commutative algebra
FractionalIdeal.mk0
{R : Type u_1} →
(K : Type u_2) →
[inst : CommRing R] →
[inst_1 : Field K] →
[inst_2 : Algebra R K] →
[inst_3 : IsFractionRing R K] →
[IsDomain R] →
[inst_5 : IsDedekindDomain R] → ↥(nonZeroDivisors (Ideal R)) →* (FractionalIdeal (nonZeroDivisors R) K)ˣSend a nonzero integral ideal to an invertible fractional ideal.
- Defined in
- Mathlib.RingTheory.ClassGroup.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- Unitsstatement · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- FractionalIdealstatement · cited by 423
Cited by15
Results whose statement or proof uses this declaration.
- ClassGroup.mk0proof · cited by 22
- NumberField.mixedEmbedding.fundamentalCone.idealSetproof · cited by 8
- ClassGroup.mk_mk0statement and proof · cited by 3
- ClassGroup.extendedHom_mk0proof · cited by 2
- FractionalIdeal.coe_mk0statement · cited by 2
- NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTopproof · cited by 1
- ClassGroup.equiv_mk0statement and proof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.mem_idealSetproof · cited by 1
- ClassGroup.mk0_integralRepproof · cited by 1
- NumberField.exists_ideal_in_class_of_norm_leproof · cited by 1
- FractionalIdeal.canonicalEquiv_mk0statement · cited by 1
- ClassGroup.mk0_eq_quotientMkstatement and proof · cited by 1