Theorems · Theorem · commutative algebra
Ideal.sInf_minimalPrimes
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R}, sInf I.minimalPrimes = I.radical- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Set.ofPredproof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- le_antisymmproof · cited by 2,068
- InfSet.sInfstatement and proof · cited by 935
- Ideal.IsPrimeproof · cited by 827
- Ideal.radicalstatement · cited by 121
- Ideal.minimalPrimesstatement and proof · cited by 74
- sInf_le_sInfproof · cited by 23
- Ideal.radical_eq_sInfproof · cited by 21
- Ideal.mem_sInfproof · cited by 15
- Ideal.exists_minimalPrimes_leproof · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.radical_map_of_mem_minimalPrimesproof · cited by 1
- Submodule.exists_eq_colon_of_mem_minimalPrimesproof · cited by 1