Intereting Posts

Is there any branch of Mathematics which has no applications in any other field or in real world?
Please explain inequality $|x^{p}-y^{p}| \leq |x-y|^p$
Solving the recurrence $t(n)=(t(n-1))^2 + 1$
Reciproc of the Lindemann theorem and the arc cosine of the golden ratio
How was Euler able to create an infinite product for sinc by using its roots?
Let $G$ be a finite group with $|G|>2$. Prove that Aut($G$) contains at least two elements.
Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
Prove that $(0)$ is a radical ideal in $\mathbb{Z}/n\mathbb{Z}$ iff $n$ is square free
If $f$ is differentiable at $x = x_0$ then $f$ is continuous at $x = x_0$.
matrix representations and polynomials
Fixed point Exercise on a compact set
How do I know when to use “let” and “suppose” in a proof?
Upper bound number of distinct prime factors
Smoothstep sigmoid-like function: Can anyone prove this relation?
Proving a sequence involved in Apéry's proof of the irrationality of $\zeta(3)$, converges

I am looking for a degree $4$ extension of $\mathbb {Q}$ with no intermediate field. I know such extension is not Galois (equivalently not normal). So I was trying to adjoin a root of an irreducible quartic. But I got stuck. Any hint/idea/solution?

- Subgroup generated by $1 - \sqrt{2}$, $2 - \sqrt{3}$, $\sqrt{3} - \sqrt{2}$
- Intuition behind “Non-Archimedean” — two senses of “non-archimedean”.
- field of algebraic numbers
- Do groups, rings and fields have practical applications in CS? If so, what are some?
- What are some algebraically closed fields?
- Find the polynomials which satisfy the condition $f(x)\mid f(x^2)$
- “Prime decomposition of $\infty$”
- Non-algebraically closed field in which every polynomial of degree $<n$ has a root
- Vakil's definition of smoothness — what happens at non-closed points?
- Does $K/E$ and $E/F$ being normal mean $K/F$ is normal?

With regard to Sebastian Schoennenbeck’s comment, an extension of $\mathbb{Q}$ with Galois group $A_4$ (alternating group on 4 points) will do the trick.

Such an extension certainly exists, in fact all alternating groups are Galois groups over $\mathbb{Q}$.

- Mean value of the rotation angle is 126.5°
- The convergence of $\sum \pm a_n$ with random signs
- How to prove that $\lim \frac{1}{n} \sqrt{(n+1)(n+2)… 2n} = \frac{4}{e}$
- Number of Ways to Fill a Matrix with symbols subject to Weird contsraint.
- Proximal mapping of $f(U) = -\log \det(U)$
- When is the moment of inertia of a smooth plane curve is maximum?
- Is $1$ a subset of $\{1\}$
- Proving connectedness of the $n$-sphere
- For which $a$ is $n\lfloor a\rfloor+1\le \lfloor na\rfloor$ true for all sufficiently large $n$?
- The smallest subobject $\sum{A_i}$ containing a family of subobjects {$A_i$}
- Pure Mathematics proof for $(-a)b$ =$-(ab)$
- Evaluate $\int_0^{2\pi}\frac{1}{1 + A\sin(\theta) + B\cos(\theta)}\, \mathrm{d}\theta \ \text{ for }\ A,B <<1$
- Does the equation $x^4+y^4+1 = z^2$ have a non-trivial solution?
- Question about a rotating cube?
- Congruence of terms