Theorems · Theorem · commutative algebra
Ideal.under_ne_bot
∀ (A : Type u_1) [inst : CommRing A] {B : Type u_2} [inst_1 : CommRing B] [inst_2 : Algebra A B]
[Algebra.IsIntegral A B] {P : Ideal B} [Nontrivial A] [IsDomain B], P ≠ ⊥ → Ideal.under A P ≠ ⊥- 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.
Cites9
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
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Nontrivialstatement and proof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- Algebra.IsIntegralstatement and proof · cited by 224
- Ideal.understatement and proof · cited by 170
- Ideal.eq_bot_of_comap_eq_botproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- isDedekindDomainDvr.of_formallyUnramifiedproof · cited by 1
- Ring.HasFiniteQuotients.of_module_finiteproof · cited by 0