Theorems · Definition · commutative algebra

Algebra.HasGoingDown.recOn

{R : Type u_1} →
  {S : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          {motive : Algebra.HasGoingDown R S → Sort u} →
            (t : Algebra.HasGoingDown R S) →
              ((exists_ideal_le_liesOver_of_lt :
                    ∀ {p : Ideal R} [p.IsPrime] (Q : Ideal S) [Q.IsPrime],
                      p < Ideal.under R Q → ∃ P ≤ Q, P.IsPrime ∧ P.LiesOver p) →
                  motive ⋯) →
                motive t

Defined in

Mathlib.RingTheory.Ideal.GoingDown

Cited by

0 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

CommRingCommRingAlgebra