Theorems · Theorem · commutative algebra
Ideal.ker_algebraMap_residueField
∀ {R : Type u_1} [inst : CommRing R] (I : Ideal R) [inst_1 : I.IsPrime], RingHom.ker (algebraMap R I.ResidueField) = I- Cited by
- 5 results in Mathlib
- Foundations
- Depth 100 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.
Cites12
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 · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.primeComplstatement · cited by 462
- RingHom.kerstatement · cited by 363
- Localization.AtPrimestatement · cited by 299
- IsLocalRing.ResidueFieldstatement · cited by 156
- Ideal.extproof · cited by 131
- Ideal.ResidueFieldstatement · cited by 119
- Ideal.algebraMap_residueField_eq_zeroproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- PrimeSpectrum.mem_image_comap_zeroLocus_sdiffproof · cited by 2
- Ideal.injective_algebraMap_quotient_residueFieldproof · cited by 1
- PrimeSpectrum.nontrivial_iff_mem_rangeComapproof · cited by 1
- isNilpotent_tensor_residueField_iffproof · cited by 1