Theorems · Theorem · commutative algebra

Module.FaithfullyFlat.isLocalRing

∀ (A : Type u_1) (B : Type u_2) [inst : CommRing A] [inst_1 : CommRing B] [inst_2 : Algebra A B]
  [Module.FaithfullyFlat A B] [IsLocalRing B], IsLocalRing A

Let B be a faithfully flat A-algebra, then A is a local ring if B is.

Defined in

Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra

Cited by

0 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraModule.FaithfullyFlatIsLocalRing