Talk:Algebraic closure

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The proof[edit]

From which book is the proof? It is not from Atiyah and MacDonald, which follows the proof from Emile Artin, but I did not check the others. (talk) 10:23, 20 November 2015 (UTC)


In what way can we speak of the algebraic closure? The K-isomorphism is non-canonical in general. -- 09:55, 30 August 2005 (UTC)

I guess that one step in the proof of the existence of an algebraic closure is missing. Namely, what you've constructed is a field, where each nonconstant polynomial from K[x] has a root. What about polynomials with coefficients from the new field? It seems that you should continue the process and then take the union, don't you? You also should mention the universal property of the algebraic closure and at least state that it holds for your construction. Sorry that I don't have time to insert this changes myself. Alexei — Preceding unsigned comment added by Stepanov239 (talkcontribs) 17:31, 17 February 2017 (UTC)

I expanded the proof. You are right. Oleg Alexandrov (talk) 01:31, 25 March 2017 (UTC)