[Merged by Bors] - feat(field_theory/splitting_field): splitting field unique #3654
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src/ring_theory/algebra_tower.lean
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| /-- If A/S/R is a tower of algebras then any S-subalgebra of A gives an R-subalgebra of A. -/ | ||
| def res (U : subalgebra S A) : subalgebra R A := | ||
| { carrier := U, | ||
| algebra_map_mem' := λ x, by { rw algebra_map_apply R S A, exact U.algebra_map_mem _ } } | ||
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| @[simp] lemma res_top : res R (⊤ : subalgebra S A) = ⊤ := | ||
| algebra.eq_top_iff.2 $ λ _, show _ ∈ (⊤ : subalgebra S A), from algebra.mem_top |
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What is the reason for renaming these? (Actually, what does res stand for?)
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shorter; restrict.
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Thanks! bors r+ |
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Main theorem:
```lean
polynomial.is_splitting_field.alg_equiv {α} (β) [field α] [field β] [algebra α β]
(f : polynomial α) [is_splitting_field α β f] : β ≃ₐ[α] splitting_field f
````
Co-authored-by: Vierkantor <Vierkantor@users.noreply.github.com>
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Main theorem:
polynomial.is_splitting_field.alg_equiv {α} (β) [field α] [field β] [algebra α β] (f : polynomial α) [is_splitting_field α β f] : β ≃ₐ[α] splitting_field f