I have some issues to prove that a basis for K over F is $\prod_{i\in S}{\sqrt{d_i}}$. I know that the basis contains $2^k$ elements but I don't know how to move on. I hope for some help!
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There is a nice hint you can use there. Have you tried following that? – Arthur Sep 24 '20 at 12:33
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Duplicate of the duplicate : https://math.stackexchange.com/questions/3837191/induction-on-k-algebra?noredirect=1#comment7915344_3837191 – GreginGre Sep 24 '20 at 12:50
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@sumi: you have already a link to answers in your previous post. There is no need to answer the same question twice. – GreginGre Sep 24 '20 at 12:51
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Does this answer your question? Induction on k algebra – GreginGre Sep 24 '20 at 12:51
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Hi GreginGre! The reason I ask the same question twice is because I didn't understand the link you gave me and because that post was old I made a new one because I don't think that anyone would reply because it hasn't been active for a long time. :) – Sumi Sep 24 '20 at 12:56
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Hi Arthur! Thank you for your answer. Isn't the hint for the first part of the question were we are trying to prove that $[K:F]=2^k$ or can it be used for the second part too? – Sumi Sep 24 '20 at 12:57