Theorems · Theorem · commutative algebra

Module.finite_iff_krullDimLE_zero

∀ (R : Type u_1) (A : Type u_2) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  [Algebra.FiniteType R A] [IsArtinianRing R], Module.Finite R A ↔ Ring.KrullDimLE 0 A

If A is a finite type algebra over an Artinian ring R, then A is finite over R if and only if dim A = 0.

Defined in

Mathlib.RingTheory.Jacobson.Artinian

Cited by

0 results in Mathlib

Foundations

Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraAlgebra.FiniteTypeIsArtinianRing