Theorems · Theorem · commutative algebra
isJacobsonRing_of_isIntegral
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[Algebra.IsIntegral R S] [IsJacobsonRing R], IsJacobsonRing S- Defined in
- Mathlib.RingTheory.Jacobson.Ring
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Top.topproof · cited by 9,680
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- Nontrivialproof · cited by 2,416
- HasQuotient.Quotientproof · cited by 2,301
- Ideal.IsPrimeproof · cited by 827
- Ideal.IsMaximalproof · cited by 452
Cited by1
Results whose statement or proof uses this declaration.
- isJacobsonRing_of_isIntegral'proof · cited by 1