Theorems · Theorem · commutative algebra

PrimeSpectrum.comap_surjective_of_faithfullyFlat

∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B]
  [Module.FaithfullyFlat A B], Function.Surjective (PrimeSpectrum.comap (algebraMap A B))

If B is a faithfully flat A-algebra, the induced map on the prime spectrum is surjective.

Defined in

Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra

Cited by

1 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraModule.FaithfullyFlat