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 October 19th, 2011, 10:48 PM #1 Member   Joined: Aug 2010 Posts: 32 Thanks: 0 Algebraic sets Here is a simple question that I could not solve it! Not yet! Well, let k be an algebraically closed field; this is the routine assumption in algebraic geometry. Let A be its associated polynomial ring, on n indeterminates, on k, and let $\mathbb{A}^n_k$ be the corresponding Affine space. Now I want an example of a non-algebraic set in $\mathbb{A}_k^n$. To be sure I can find some examples when k is the complex field and n=1,2. But here I want an example that works for any field k (but algebraically closed of course) and arbitrary n. I'd be grateful if anyone can help me with this!
 October 22nd, 2011, 08:04 PM #2 Senior Member   Joined: Nov 2010 From: Berkeley, CA Posts: 174 Thanks: 35 Math Focus: Elementary Number Theory, Algebraic NT, Analytic NT Re: Algebraic sets Does $\mathbb{A}_k^n \ - \ \{(0, \ 0, \ \dots, \ 0\)}$ work?

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