Theorems · Theorem · commutative algebra
minimalPrimes_eq_minimals
∀ {R : Type u_1} [inst : CommSemiring R], minimalPrimes R = {x | Minimal Ideal.IsPrime x}- Cited by
- 4 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.ofPredstatement · cited by 6,101
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Minimalstatement and proof · cited by 150
- minimalPrimesstatement · cited by 32
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.height_eq_zero_iffproof · cited by 5
- Ideal.mem_minimalPrimes_of_krullDimLE_zeroproof · cited by 2
- IsLocalization.subsingleton_primeSpectrum_of_mem_minimalPrimesproof · cited by 2
- PrimeSpectrum.vanishingIdeal_irreducibleComponentsproof · cited by 2