Theorems · Theorem · commutative algebra
RingHom.ker_eq_comap_bot
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S]
[rcf : RingHomClass F R S] (f : F), RingHom.ker f = Ideal.comap f ⊥- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Idealstatement · cited by 4,748
- Bot.botstatement · cited by 4,720
- FunLikestatement and proof · cited by 2,560
- Ideal.comapstatement · cited by 443
- RingHom.kerstatement · cited by 363
- RingHomClassstatement and proof · cited by 193
Cited by23
Results whose statement or proof uses this declaration.
- RingHom.comap_kerproof · cited by 16
- Algebra.FinitePresentation.equivproof · cited by 9
- Ideal.mem_quotient_iff_mem_supproof · cited by 3
- Ideal.minimalPrimes_comap_of_surjectiveproof · cited by 3
- Ideal.minimalPrimes_eq_comapproof · cited by 2
- Algebra.WeaklyQuasiFiniteAt.baseChangeproof · cited by 2
- Ideal.jacobson_eq_iff_jacobson_quotient_eq_botproof · cited by 2
- Ideal.ker_quotientMap_mkproof · cited by 1
- Ideal.map_eq_iff_sup_ker_eq_of_surjectiveproof · cited by 1
- PrimeSpectrum.vanishingIdeal_range_comapproof · cited by 1
- Algebra.Generators.comp_localizationAway_kerproof · cited by 1
- Ideal.mem_minimalPrimes_span_of_mem_minimalPrimes_span_insertproof · cited by 1