Theorems · Theorem · commutative algebra
Ideal.mem_minimalPrimes_of_krullDimLE_zero
∀ {R : Type u_1} [inst : CommSemiring R] [Ring.KrullDimLE 0 R] (I : Ideal R) [I.IsPrime], I ∈ minimalPrimes R- Defined in
- Mathlib.RingTheory.KrullDimension.Basic
- Cited by
- 2 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Eq.geproof · cited by 375
- Ring.KrullDimLEstatement and proof · cited by 79
- Ideal.IsMaximal.eq_of_leproof · cited by 39
- Ideal.IsPrime.ne_top'proof · cited by 38
- minimalPrimesstatement · cited by 32
- minimalPrimes_eq_minimalsproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- IsNoetherianRing.isArtinianRing_of_krullDimLE_zeroproof · cited by 2
- Ideal.mem_minimalPrimes_iff_isPrimeproof · cited by 1