Theorems · Theorem · commutative algebra
Ideal.ne_bot_of_liesOver_of_ne_bot
∀ {A : Type u_2} {B : Type u_3} [inst : CommSemiring A] [inst_1 : Semiring B] [inst_2 : Algebra A B] [FaithfulSMul A B]
{p : Ideal A}, p ≠ ⊥ → ∀ (P : Ideal B) [P.LiesOver p], P ≠ ⊥- Defined in
- Mathlib.RingTheory.Ideal.Over
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- FaithfulSMulstatement and proof · cited by 340
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.underproof · cited by 170
- Ideal.over_defproof · cited by 60
- Ideal.under_botproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.ne_bot_of_mem_primesOverproof · cited by 3
- Ideal.ramificationIdx'_algebra_tower'proof · cited by 1
- Algebra.isUnramifiedIn_iff_forall_of_isDedekindDomain'proof · cited by 1
- Algebra.IsUnramifiedAt.of_liesOverproof · cited by 0