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[Merged by Bors] - feat(field_theory/algebraic_closure): algebraic closure #3733
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Delighted to see this. I was literally just looking for the definition of algebraically closed fields three days ago, when writing this. Looking forward to updating one this merges. |
Vierkantor
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Aug 11, 2020
| @@ -321,6 +321,8 @@ begin | |||
| ... ≤ v (a + s) : aux (a + s) (-s) (by rwa ←ideal.neg_mem_iff at h) | |||
| end | |||
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| local attribute [-instance] classical.DLO | |||
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Could you add a comment (linking to Zulip?) explaining why this instance is problematic here?
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kckennylau
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Aug 11, 2020
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| - `is_alg_closure k K` is the typeclass saying `K` is an algebraic closure of `k`. | ||
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| - `algebraic_closure k` is an algebraic closure of `k` (in the same universe). | ||
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Could you add a description of the construction you are using, and a bibliography reference if you followed a book or paper? There are many ways to prove this theorem and it would help to know which one you use.
kckennylau
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Aug 12, 2020
Vierkantor
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Thanks! bors r+ |
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👎 Rejected by label |
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```lean instance : is_alg_closed (algebraic_closure k) := ``` TODO: Show that any algebraic extension embeds into any algebraically closed extension (via Zorn's lemma). Co-authored-by: Patrick Massot <patrickmassot@free.fr>
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Pull request successfully merged into master. Build succeeded: |
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instance : is_alg_closed (algebraic_closure k) :=TODO: Show that any algebraic extension embeds into any algebraically closed extension (via Zorn's lemma).