Theorems · Theorem · commutative algebra
Ideal.injective_algebraMap_quotient_residueField
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) [inst_1 : I.IsPrime],
Function.Injective ⇑(algebraMap (R ⧸ I) I.ResidueField)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIdeal.IsPrime
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapstatement and proof · cited by 4,706
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Ideal.IsPrimestatement and proof · cited by 827
- RingHomClass.toRingHomproof · cited by 746
- Ideal.mapproof · cited by 692
- Ideal.Quotient.mkproof · cited by 610
- Ideal.primeComplstatement · cited by 462
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.bijective_algebraMap_quotient_residueFieldproof · cited by 1