[Merged by Bors] - feat(Mathlib/RingTheory/Ideal/QuotientOperations): First Isomorphism Theorem for algebras #11027
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…Theorem for algebras (#11027) We add the First Isomorphism Theorem for algebras. (only the surjective version was present in mathlib). We also adjust the docstring on top of the file. Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>
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| {A B : Type*} [CommRing A] [Algebra R A] [Semiring B] [Algebra R B] | ||
| (f : A →ₐ[R] B) : | ||
| (A ⧸ RingHom.ker f) ≃ₐ[R] f.range := |
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| fun ⟨_y, hy⟩ => | ||
| let ⟨x, hx⟩ := hy | ||
| ⟨x, SetCoe.ext hx⟩ |
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| fun ⟨_y, hy⟩ => | |
| let ⟨x, hx⟩ := hy | |
| ⟨x, SetCoe.ext hx⟩ | |
| RingHom.rangeRestrict_surjective f |
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| theorem ker_rangeRestrict (f : A →ₐ[R] B) : | ||
| RingHom.ker f.rangeRestrict = RingHom.ker f := | ||
| Ideal.ext fun _ ↦ Subtype.ext_iff |
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| Ideal.ext fun _ ↦ Subtype.ext_iff | |
| rfl |
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Pull request successfully merged into master. Build succeeded: |
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…Theorem for algebras (#11027) We add the First Isomorphism Theorem for algebras. (only the surjective version was present in mathlib). We also adjust the docstring on top of the file. Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>
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…Theorem for algebras (#11027) We add the First Isomorphism Theorem for algebras. (only the surjective version was present in mathlib). We also adjust the docstring on top of the file. Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>
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…Theorem for algebras (#11027) We add the First Isomorphism Theorem for algebras. (only the surjective version was present in mathlib). We also adjust the docstring on top of the file. Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>
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…Theorem for algebras (#11027) We add the First Isomorphism Theorem for algebras. (only the surjective version was present in mathlib). We also adjust the docstring on top of the file. Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>
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We add the First Isomorphism Theorem for algebras.
(only the surjective version was present in mathlib).
We also adjust the docstring on top of the file.