Exemplu de extindere

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Cezar Lupu
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Exemplu de extindere

Post by Cezar Lupu »

Dati exemplu de o extindere \( K\supset\mathbb{Q} \) astfel incat \( [K:\mathbb{Q}(\sqrt{2})]=5 \).
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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Beniamin Bogosel
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Post by Beniamin Bogosel »

Se poate \( \mathbb{Q}(\sqrt[10]{2}) \), cred. Avem \( \mathbb{Q}(\sqrt[10]{2})\supset \mathbb{Q}(\sqrt{2}) \) si \( [\mathbb{Q}(\sqrt[10]{2}):\mathbb{Q}]=10,\ [\mathbb{Q}(\sqrt{2}):\mathbb{Q}]=2 \), adica \( [\mathbb{Q}(\sqrt[10]{2}) ,\mathbb{Q}(\sqrt{2})]=5 \).
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