Theorems · Theorem · commutative algebra
Ideal.ResidueField.ringHom_ext
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {I : Ideal R} [inst_2 : I.IsPrime]
{f g : I.ResidueField →+* S}, f.comp (algebraMap R I.ResidueField) = g.comp (algebraMap R I.ResidueField) → f = g- Cited by
- 3 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- HasQuotient.Quotientproof · cited by 2,301
- RingHom.compstatement and proof · cited by 899
- nonZeroDivisorsproof · cited by 895
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplstatement · cited by 462
- Localization.AtPrimestatement · cited by 299
- Ideal.ResidueFieldstatement and proof · cited by 119
- IsLocalization.ringHom_extproof · cited by 32
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.ResidueField.algHom_extproof · cited by 7
- Ideal.Fiber.lift_residueField_surjectiveproof · cited by 1
- Ideal.ResidueField.ringHom_ext_iffproof · cited by 0