Theorems · Theorem · commutative algebra
Ideal.IsIntegral.eq_bot_of_comap_eq_bot
∀ (R : Type u_1) [inst : CommRing R] {A : Type u_3} [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.IsIntegral R A] [IsDomain A] [Nontrivial R] {I : Ideal A}, Ideal.comap (algebraMap R A) I = ⊥ → I = ⊥- Defined in
- Mathlib.RingTheory.Ideal.GoingUp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Bot.botstatement · cited by 4,720
- Algebra.algebraMapstatement · cited by 4,706
- Nontrivialstatement and proof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- Ideal.comapstatement · cited by 443
- Algebra.IsIntegralstatement and proof · cited by 224
- Ideal.IsIntegral.comap_ne_botproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.IntegralClosure.eq_bot_of_comap_eq_botproof · cited by 0
- Ideal.IsIntegralClosure.eq_bot_of_comap_eq_botproof · cited by 0