Theorems · Theorem · commutative algebra

Module.associatedPrimes.minimalPrimes_annihilator_subset_associatedPrimes

∀ (R : Type u_1) [inst : CommRing R] (M : Type u_3) [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsNoetherianRing R]
  [Module.Finite R M], (Module.annihilator R M).minimalPrimes ⊆ associatedPrimes R M

Defined in: Mathlib.RingTheory.Ideal.AssociatedPrime.Localization
Cited by: 0 results in Mathlib
Foundations: Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module IsNoetherianRing Module.Finite

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Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
SetLike.coeproof · cited by 8,199
Idealstatement and proof · cited by 4,748
Algebra.algebraMapproof · cited by 4,706
Nontrivialproof · cited by 2,416
Disjointproof · cited by 2,201
Module.Finitestatement and proof · cited by 1,032
Ideal.IsPrimeproof · cited by 827
Ideal.primeComplproof · cited by 462

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