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- #1

- Jun 22, 2012

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Example 14 on page 282 (see attachment) reads as follows:

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**Example 14.**Let [TEX] E \supseteq F [/TEX] be fields and let [TEX] u, v \in E [/TEX].

If u and u + v are algebraic over F, show that v is algebraic over F.

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In the solution, Nicholson writes the following:

**Solution.**Write L = F(u + v) so that L(u) = F(u, v). ... ... etc etc

Can someone please show me (formally and exactly) why [TEX] L = F(u + v) \Longrightarrow L(u) = F(u, v) [/TEX].

Peter

[This has also been posted on MHF]