List questions from normal-extension | MathQA

What does an embedding over $K$ mean?

Published on 16 Feb 2022 - 21:32

Splitting fields are normal using symmetric polynomials.

Published on 27 Feb 2022 - 22:41

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

Published on 20 Apr 2022 - 18:36

Non-normal extension of Q

Published on 29 May 2022 - 2:35

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

Published on 08 Jun 2022 - 11:49

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 16 Jun 2022 - 8:58

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

Published on 17 Jun 2022 - 17:07

Simple normal extension

Published on 06 Dec 2022 - 19:10

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

Published on 02 Jan 2023 - 16:58

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

Published on 21 Jan 2023 - 17:30