Theorems · Theorem · commutative algebra
Ideal.comap_jacobson
∀ {R : Type u} {S : Type v} [inst : Ring R] [inst_1 : Ring S] {f : R →+* S} {K : Ideal S},
Ideal.comap f K.jacobson = sInf (Ideal.comap f '' {J | K ≤ J ∧ J.IsMaximal})- Defined in
- Mathlib.RingTheory.Jacobson.Ideal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Set.ofPredstatement and proof · cited by 6,101
- Set.imagestatement · cited by 5,609
- Idealstatement and proof · cited by 4,748
- InfSet.sInfstatement · cited by 935
- Ideal.IsMaximalstatement and proof · cited by 452
- Ideal.comapstatement · cited by 443
- Ideal.jacobsonstatement · cited by 88
- sInf_eq_iInfproof · cited by 22
- Ideal.comap_sInf'proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- isJacobsonRing_of_isIntegralproof · cited by 1
- Polynomial.jacobson_bot_of_integral_localizationproof · cited by 0