Theorems · Theorem · commutative algebra
Ring.KrullDimLE.isField_of_isReduced
∀ {R : Type u_1} [inst : CommSemiring R] [Ring.KrullDimLE 0 R] [IsReduced R] [IsLocalRing R], IsField R- Defined in
- Mathlib.RingTheory.KrullDimension.Zero
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- IsLocalRingstatement and proof · cited by 339
- IsFieldstatement · cited by 103
- IsReducedstatement and proof · cited by 98
- Ring.KrullDimLEstatement and proof · cited by 79
- Ideal.zero_eq_botproof · cited by 27
- IsLocalRing.isField_iff_maximalIdeal_eqproof · cited by 8
- nilradical_eq_zeroproof · cited by 3
- Ring.KrullDimLE.nilradical_eq_maximalIdealproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- isStronglyTranscendental_mk_of_mem_minimalPrimesproof · cited by 1
- PrimeSpectrum.subsingleton_iff_isField_of_isReducedproof · cited by 1