Theorems · Theorem · commutative algebra
Ideal.radical_eq_jacobson
∀ {R : Type u_1} [inst : CommRing R] [H : IsJacobsonRing R] (I : Ideal R), I.radical = I.jacobson- Defined in
- Mathlib.RingTheory.Jacobson.Ring
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsJacobsonRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Set.ofPredproof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- le_antisymmproof · cited by 2,068
- Ideal.IsMaximalproof · cited by 452
- Ideal.radicalstatement and proof · cited by 121
- Ideal.jacobsonstatement · cited by 88
- Ideal.IsMaximal.isPrimeproof · cited by 53
- le_sInfproof · cited by 51
- IsJacobsonRingstatement and proof · cited by 40
- Ideal.le_radicalproof · cited by 16
- Ideal.IsPrime.radical_le_iffproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.vanishingIdeal_zeroLocus_eq_radicalproof · cited by 1
- PrimeSpectrum.exists_isClosed_singleton_of_isJacobsonRingproof · cited by 1