List questions from normal-extension | MathQA

What does an embedding over $K$ mean?

Published on 23 Feb 2026 - 8:20

Splitting fields are normal using symmetric polynomials.

Published on 23 Feb 2026 - 8:19

Find a particular intermediate field $M$ such that $\mathbb{Q}\subset M\subset\mathbb{Q}(\sqrt{\frac{3+i\sqrt{7}}{2}})$.

Published on 23 Feb 2026 - 8:26

Non-normal extension of Q

Published on 23 Feb 2026 - 8:28

Root of the polynomial $x^3-x-1$ over $\mathbb{Q}$ does not generate normal extension

Published on 23 Feb 2026 - 8:24

Show that there exist $K_0 = \mathbb Q ⊆ K_1 ⊆ K_2 ⊆ K_3 ⊆ K_4 = L$ , where, for $i = 1, . . . , 4$ , $|K_i : K_{i−1}| = 3$.

Published on 23 Feb 2026 - 8:27

Is the extension $\mathbb{Q}(\sqrt{7+\sqrt{7}})/\mathbb{Q}$ a Galois extension?

Published on 23 Feb 2026 - 8:24

Simple normal extension

Published on 23 Feb 2026 - 8:18

Show there is a tower of cyclic field extensions of prime degree from $\mathbb{Q}(\sqrt[12]{5})$ to $\mathbb{Q}$

Published on 23 Feb 2026 - 8:27

Why isn’t $\mathbb{Q}[x]/\langle x^3-2\rangle$ a normal extension over $\mathbb{Q}$?

Published on 23 Feb 2026 - 8:23