Theorems · Theorem · commutative algebra
Ideal.minimalPrimes_eq_subsingleton
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R}, I.IsPrimary → I.minimalPrimes = {I.radical}- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites15
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
- Set.extproof · cited by 2,266
- Ideal.IsPrimeproof · cited by 827
- LE.le.antisymmproof · cited by 507
- Ideal.radicalstatement and proof · cited by 121
- Ideal.minimalPrimesstatement and proof · cited by 74
- Membership.mem.outproof · cited by 38
- Ideal.IsMinimalPrime.isPrimeproof · cited by 26
- Ideal.IsMinimalPrime.leproof · cited by 23
- Ideal.le_radicalproof · cited by 16
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