Theorems · Theorem · commutative algebra
isAssociatedPrime_iff_exists_injective_linearMap
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) (M : Type u_2) [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[IsNoetherianRing R], IsAssociatedPrime I M ↔ I.IsPrime ∧ ∃ f, Function.Injective ⇑f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- HasQuotient.Quotientstatement and proof · cited by 2,301
- LinearMap.compproof · cited by 1,642
- one_smulproof · cited by 1,374
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