Theorems · Theorem · commutative algebra
Ideal.isPrimary_of_isMaximal_radical
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R}, I.radical.IsMaximal → I.IsPrimary- Defined in
- Mathlib.RingTheory.Ideal.IsPrimary
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Ideal.spanproof · cited by 948
- Ideal.IsMaximalstatement and proof · cited by 452
- mul_addproof · cited by 413
- Ideal.radicalstatement and proof · cited by 121
- Ideal.IsMaximal.isPrimeproof · cited by 53
- Ideal.exists_le_maximalproof · cited by 47
- Ideal.mul_topproof · cited by 42
- Ideal.IsMaximal.ne_topproof · cited by 42
- Ideal.IsMaximal.eq_of_leproof · cited by 39
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