Theorems · Theorem · commutative algebra
Ideal.IntegralClosure.comap_ne_bot
Deprecated since 2026-05-08Use Ideal.IsIntegral.comap_ne_bot instead.
∀ (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}, I ≠ ⊥ → Ideal.comap (algebraMap R A) I ≠ ⊥Alias of Ideal.IsIntegral.comap_ne_bot.
- Defined in
- Mathlib.RingTheory.Ideal.GoingUp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement · cited by 17,173
- Algebrastatement · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- Algebra.algebraMapstatement · cited by 4,706
- Nontrivialstatement · cited by 2,416
- IsDomainstatement · cited by 2,196
- Ideal.comapstatement · cited by 443
- Algebra.IsIntegralstatement · cited by 224
- Ideal.IsIntegral.comap_ne_botproof · cited by 4
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