Theorems · Theorem · commutative algebra
Ideal.minimalPrimes_eq_empty_iff
∀ {R : Type u_1} [inst : CommSemiring R] (I : Ideal R), I.minimalPrimes = ∅ ↔ I = ⊤- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Ideal.IsMaximalproof · cited by 452
- Ideal.minimalPrimesstatement and proof · cited by 74
- Ideal.exists_le_maximalproof · cited by 47
- Set.notMem_emptyproof · cited by 35
- Ideal.exists_minimalPrimes_leproof · cited by 14
- Ideal.minimalPrimes_topproof · cited by 4
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