Ideal.IsMaximal.mem_associatedPrimes_of_isFractionRing

∀ (A : Type u) [inst : CommRing A] [IsNoetherianRing A] [IsFractionRing A A] (I : Ideal A) [hI : I.IsMaximal],
  I ∈ associatedPrimes A A

Every maximal ideal of a commutative Noetherian total ring of fractions A is an associated prime of the A-module A.

Defined in: Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness
Cited by: 0 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsNoetherianRing IsFractionRing Ideal.IsMaximal

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.

Nothing cites this yet.