Theorems · Theorem · commutative algebra
Algebra.HasGoingDown.exists_ideal_le_liesOver_of_lt
∀ {R : Type u_1} {S : Type u_2} {inst : CommRing R} {inst_1 : CommRing S} {inst_2 : Algebra R S}
[self : Algebra.HasGoingDown R S] {p : Ideal R} [p.IsPrime] (Q : Ideal S) [Q.IsPrime],
p < Ideal.under R Q → ∃ P ≤ Q, P.IsPrime ∧ P.LiesOver p- Defined in
- Mathlib.RingTheory.Ideal.GoingDown
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 4,748
- Ideal.IsPrimestatement · cited by 827
- Ideal.LiesOverstatement · cited by 272
- Ideal.understatement · cited by 170
- Algebra.HasGoingDownstatement and proof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.exists_ideal_le_liesOver_of_leproof · cited by 2