Theorems · Theorem · commutative algebra
isJacobsonRing_localization
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] (y : R) [inst_2 : Algebra R S]
[IsLocalization.Away y S] [H : IsJacobsonRing R], IsJacobsonRing SIf S is the localization of the Jacobson ring R at the submonoid generated by y : R, then
S is Jacobson.
- Defined in
- Mathlib.RingTheory.Jacobson.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
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
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- LE.le.transproof · cited by 3,151
- Disjointproof · cited by 2,201
- le_antisymmproof · cited by 2,068
- iInfproof · cited by 1,690
- le_transproof · cited by 985
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.jacobson_bot_of_integral_localizationproof · cited by 0