Theorems · Theorem · commutative algebra
Ring.KrullDimLE.isField_of_isDomain
∀ {R : Type u_1} [inst : CommSemiring R] [Ring.KrullDimLE 0 R] [IsDomain R], IsField R- Defined in
- Mathlib.RingTheory.KrullDimension.Zero
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 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.
- CommSemiringstatement and proof · cited by 10,911
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- Ideal.IsPrimeproof · cited by 827
- bot_leproof · cited by 306
- IsFieldstatement and proof · cited by 103
- Ideal.IsPrime.ne_topproof · cited by 82
- Ring.KrullDimLEstatement and proof · cited by 79
- Ideal.IsMaximal.eq_of_leproof · cited by 39
- Ring.not_isField_iff_exists_primeproof · cited by 4
- Ideal.IsPrime.isMaximal'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsPrincipalIdealRing.ringKrullDim_eq_oneproof · cited by 1
- IsDiscreteValuationRing.ringKrullDim_eq_oneproof · cited by 1
- ringKrullDim_eq_one_iff_of_isLocalRing_isDomainproof · cited by 0