Theorems · Theorem · commutative algebra
Ring.KrullDimLE.existsUnique_isPrime
∀ (R : Type u_1) [inst : CommSemiring R] [Ring.KrullDimLE 0 R] [IsLocalRing R], ∃! I, I.IsPrime
- Defined in
- Mathlib.RingTheory.KrullDimension.Zero
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- Idealstatement · cited by 4,748
- Ideal.IsPrimestatement · cited by 827
- IsLocalRingstatement and proof · cited by 339
- ExistsUniquestatement · cited by 268
- List.TFAE.outproof · cited by 177
- Ring.KrullDimLEstatement and proof · cited by 79
- Ring.krullDimLE_zero_and_isLocalRing_tfaeproof · cited by 7
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