Theorems · Theorem · commutative algebra
IsAssociatedPrime.map_of_injective
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R} {M : Type u_2} [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{M' : Type u_3} [inst_3 : AddCommMonoid M'] [inst_4 : Module R M'] (f : M →ₗ[R] M'),
IsAssociatedPrime I M → Function.Injective ⇑f → IsAssociatedPrime I M'- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Ideal.extproof · cited by 131
- Ideal.radicalproof · cited by 121
- Submodule.colonproof · cited by 80
- map_eq_zero_iffproof · cited by 62
Cited by2
Results whose statement or proof uses this declaration.
- associatedPrimes.subset_of_injectiveproof · cited by 2
- LinearEquiv.isAssociatedPrime_iffproof · cited by 0