Theorems · Definition · commutative algebra

Algebra.IsGeometricallyReduced.casesOn

{R : Type u_3} →
  {A : Type u_4} →
    [inst : CommRing R] →
      [inst_1 : Ring A] →
        [inst_2 : Algebra R A] →
          {motive : Algebra.IsGeometricallyReduced R A → Sort u} →
            (t : Algebra.IsGeometricallyReduced R A) →
              ((isReduced_algebraicClosure_tensorProduct :
                    ∀ (p : Ideal R) [inst_3 : p.IsPrime],
                      IsReduced (TensorProduct R (AlgebraicClosure p.ResidueField) A)) →
                  motive ⋯) →
                motive t

Defined in

Mathlib.RingTheory.Nilpotent.GeometricallyReduced

Cited by

1 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingRingAlgebra