Theorems · Theorem · commutative algebra

Module.supportDim_eq_ringKrullDim_quotient_annihilator

∀ (R : Type u_1) [inst : CommRing R] (M : Type u_2) [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Finite R M],
  Module.supportDim R M = ringKrullDim (R ⧸ Module.annihilator R M)

Defined in

Mathlib.RingTheory.KrullDimension.Module

Cited by

2 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.Finite