Theorems · Inductive type · commutative algebra
Ring.DimensionLEOne
(R : Type u_1) → [CommRing R] → Prop
A ring R has Krull dimension at most one if all nonzero prime ideals are maximal.
- Defined in
- Mathlib.RingTheory.DedekindDomain.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement · cited by 17,173
Cited by16
Results whose statement or proof uses this declaration.
- Ideal.IsPrime.isMaximalstatement and proof · cited by 24
- IsIntegralClosure.isDedekindDomainproof · cited by 7
- Ring.DimensionLEOne.maximalOfPrimestatement and proof · cited by 6
- Ring.DimensionLEOne.not_lt_ltstatement and proof · cited by 2
- Ring.DimensionLEOne.of_isIntegralstatement and proof · cited by 2
- Ring.DimensionLEOne.localizationstatement and proof · cited by 1
- Ring.DimensionLeOne.prime_le_prime_iff_eqstatement and proof · cited by 1
- isDedekindDomain_iffstatement and proof · cited by 1
- Ring.DimensionLEOne.casesOnstatement and proof · cited by 0
- Ring.DimensionLEOne.eq_bot_of_ltstatement and proof · cited by 0
- Ring.DimensionLEOne.isIntegralClosurestatement · cited by 0
- Ring.DimensionLEOne.of_ringEquivstatement and proof · cited by 0