Theorems · Theorem · commutative algebra
IsFractionRing.isUnit_den_iff
∀ {A : Type u_1} [inst : CommRing A] [inst_1 : IsDomain A] [inst_2 : UniqueFactorizationMonoid A] {K : Type u_2}
[inst_3 : Field K] [inst_4 : Algebra A K] [inst_5 : IsFractionRing A K] (x : K),
IsUnit ↑(IsFractionRing.den A x) ↔ IsLocalization.IsInteger A x- Defined in
- Mathlib.RingTheory.Localization.NumDen
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
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
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement · cited by 3,086
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- IsUnitstatement and proof · cited by 1,602
- map_mulproof · cited by 1,137
- nonZeroDivisorsstatement · cited by 895
- IsFractionRingstatement and proof · cited by 738
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