Theorems · Theorem · commutative algebra
Ideal.IsIntegral.comap_ne_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}, I ≠ ⊥ → Ideal.comap (algebraMap R A) I ≠ ⊥- Defined in
- Mathlib.RingTheory.Ideal.GoingUp
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 4,720
- Algebra.algebraMapstatement and proof · cited by 4,706
- Nontrivialstatement and proof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- Ideal.comapstatement and proof · cited by 443
- Algebra.IsIntegralstatement and proof · cited by 224
- Algebra.IsIntegral.isIntegralproof · cited by 86
- Submodule.ne_bot_iffproof · cited by 28
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.IsIntegral.eq_bot_of_comap_eq_botproof · cited by 2
- Ring.DimensionLEOne.of_isIntegralproof · cited by 2
- Ideal.IsIntegralClosure.comap_ne_botproof · cited by 0
- Ideal.IntegralClosure.comap_ne_botproof · cited by 0