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Results tagged with number-fields
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user 17907
1
vote
Irreducibility of polynomials over some number fields
Here is a different approach, which is arguably a bit more elementary. If $f=X^n-p$ splits in $K$, and $g$ is one of its factors, then the constant term of $g$, being a product of zeros of $f$, must b …
- 4,746
7
votes
Accepted
Square root in number field
This answer is meant to answer only your second question.
Claim. Let $K=\mathbb{Q}(\sqrt[3]{2})$ and $\alpha = \sqrt[3]{2}-\sqrt[3]{4} \in K$. Then there does not exist $\beta \in K$ such that $\beta^ …
- 4,746