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- #1

- Jun 22, 2012

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Example 13 on page 282 (see attachment) reads as follows:

"If [TEX] u = \sqrt[3]{2} [/TEX] show that [TEX] \mathbb{Q}(u) = \mathbb{Q}(u^2) [/TEX]"

In the third line of the explanation - see page 282 of attachment - we read:

"But [TEX] [\mathbb{Q}(u^2) \ : \ \mathbb{Q}] \ne 1 [/TEX] because [TEX] u^2 \notin \mathbb{Q} [/TEX] ... ... "

Can someone explain why it follows that [TEX] u^2 \notin \mathbb{Q} \Longrightarrow [\mathbb{Q}(u^2) \ : \ \mathbb{Q}] \ne 1 [/TEX]

Peter

[This has also been posted on MHF]