Theorems · Theorem · commutative algebra
Ideal.ker_le_comap
∀ {R : Type u_1} {S : Type u_2} {F : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S]
[rc : RingHomClass F R S] {K : Ideal S} (f : F), RingHom.ker f ≤ Ideal.comap f K- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- Ideal.comapstatement · cited by 443
- RingHom.kerstatement and proof · cited by 363
- RingHomClassstatement and proof · cited by 193
- Ideal.mem_comapproof · cited by 54
- RingHom.mem_kerproof · cited by 49
- Ideal.zero_memproof · cited by 37
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.ker_applyproof · cited by 14
- AlgebraicGeometry.Scheme.Hom.le_ker_compproof · cited by 5
- isJacobsonRing_of_surjectiveproof · cited by 4
- Ideal.exists_ideal_over_prime_of_isIntegral_of_isPrimeproof · cited by 2
- IsLocalRing.quotient_artinian_of_mem_minimalPrimes_of_isLocalRingproof · cited by 1
- Ideal.mem_minimalPrimes_span_of_mem_minimalPrimes_span_insertproof · cited by 1
- Ideal.ncard_primesOver_lt_of_not_leproof · cited by 1
- Ideal.map_height_le_one_of_mem_minimalPrimesproof · cited by 1