Theorems · Theorem · commutative algebra
RingHom.map_pullbackSnd_ker_pullbackFst_eq
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : Ring R] [inst_1 : Ring S] [inst_2 : Semiring T] (f : R →+* T)
(g : S →+* T), Ideal.map (f.pullbackSnd g) (RingHom.ker (f.pullbackFst g)) = RingHom.ker g- Defined in
- Mathlib.RingTheory.LocalRing.Pullback
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement · cited by 4,748
- le_antisymmproof · cited by 2,068
- Ideal.mapstatement · cited by 692
- Subringstatement · cited by 602
- RingHom.kerstatement and proof · cited by 363
- Ideal.mem_map_of_memproof · cited by 71
- Ideal.map_le_iff_le_comapproof · cited by 60
- RingHom.pullbackstatement and proof · cited by 6
- RingHom.pullbackFststatement · cited by 4
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