Theorems · Theorem · commutative algebra

IsAssociatedPrime.annihilator_le

∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R} {M : Type u_2} [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
  IsAssociatedPrime I M → ⊤.annihilator ≤ I

Defined in: Mathlib.RingTheory.Ideal.AssociatedPrime.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring AddCommMonoid Module

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Modulestatement and proof · cited by 20,661
AddCommMonoidstatement and proof · cited by 12,281
CommSemiringstatement and proof · cited by 10,911
Top.topstatement and proof · cited by 9,680
Submodulestatement · cited by 7,192
Idealstatement and proof · cited by 4,748
Bot.botproof · cited by 4,720
LE.le.transproof · cited by 3,151
Ideal.IsPrimeproof · cited by 827
le_topproof · cited by 411
Ideal.radicalproof · cited by 121
Submodule.colonproof · cited by 80

Cited by1

Results whose statement or proof uses this declaration.

Module.associatedPrimes.minimalPrimes_annihilator_subset_associatedPrimesproof · cited by 0