Theorems · Theorem · commutative algebra
RingHom.quotientKerEquivOfSurjective_symm_comp
∀ {R : Type u} {S : Type v} [inst : Ring R] [inst_1 : Semiring S] {f : R →+* S} (hf : Function.Surjective ⇑f),
(RingHom.quotientKerEquivOfSurjective hf).symm.toRingHom.comp f = Ideal.Quotient.mk (RingHom.ker f)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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
- HasQuotient.Quotientstatement · cited by 2,301
- RingHom.compstatement · cited by 899
- Ideal.Quotient.mkstatement and proof · cited by 610
- RingEquiv.symmstatement · cited by 567
- RingHom.kerstatement and proof · cited by 363
- RingHom.extproof · cited by 331
- RingEquiv.toRingHomstatement · cited by 150
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