Theorems · Definition · commutative algebra
associatedPrimes
(R : Type u_1) → [inst : CommSemiring R] → (M : Type u_2) → [inst_1 : AddCommMonoid M] → [Module R M] → Set (Ideal R)
The set of associated primes of a module.
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Set.ofPredproof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- IsAssociatedPrimeproof · cited by 12
Cited by21
Results whose statement or proof uses this declaration.
- associatedPrimes.nonemptystatement · cited by 4
- AssociatedPrimes.mem_iffstatement · cited by 3
- associatedPrimes.finitestatement and proof · cited by 3
- biUnion_associatedPrimes_eq_compl_nonZeroDivisorsstatement · cited by 2
- biUnion_associatedPrimes_eq_zero_divisorsstatement · cited by 2
- Module.associatedPrimes.mem_associatedPrimes_of_comap_mem_associatedPrimes_of_isLocalizedModulestatement and proof · cited by 2
- IsSMulRegular.subsingleton_linearMap_iffproof · cited by 2
- associatedPrimes.subset_of_injectivestatement and proof · cited by 2
- associatedPrimes.subset_union_of_exactstatement and proof · cited by 2
- biUnion_associatedPrimes_eq_compl_regularstatement · cited by 1
- Ideal.bot_lt_annihilator_of_disjoint_nonZeroDivisorsproof · cited by 1
- Module.associatedPrimes.comap_mem_associatedPrimes_of_mem_associatedPrimes_of_isLocalizedModule_of_fgstatement and proof · cited by 1