Intereting Posts

$\int_{0}^{\infty}\frac{dx}{1+x^n}$
Convergence of $\int_{1}^{\infty} \frac{\sin x}{x^{\alpha}}dx$
$K/\langle x^2-y^3\rangle \cong K$
Reference request: toric geometry
Why isn't $\mathbb{R}^2$ a countable union of ranges of curves?
How can I express $\sum_{k=0}^n\binom{-1/2}{k}(-1)^k\binom{-1/2}{n-k}$ without using summations or minus signs?
Let $k \geq 3$; prove $2^k$ can be written as $(2m+1)^2+7(2n+1)^2$
Arbitrage opportunity
Can I apply the Girsanov theorem to an Ornstein-Uhlenbeck process?
Rational Roots of Riemann's $\zeta$ Function
How to obtain asymptotes of this curve?
Showing the 3D Ricci flow ODE preserves the order of the curvature tensor eigenvalues
Strongly complete profinite group
Evaluate the integration : $\int\sqrt{\frac{(1-\sin x)(2-\sin x)}{(1+\sin x)(2+\sin x)}}dx$
Is there a conjecture with maximal prime gaps

Suppose that F is a field contained in an algebraically closed field A. Prove that every automorphism of F can be extended to an automorphism of A.

- Minimal polynomials
- How to determine the Galois group of irreducible polynomials of degree $3,4,5$
- A field that is an ordered field in two distinct ways
- When are nonintersecting finite degree field extensions linearly disjoint?
- Are distinct prime ideals in a ring always coprime? If not, then when are they?
- Complex Galois Representations are Finite
- Polynomials having as roots the sum (respectively, the product) of two algebraic elements
- Quartic Equation having Galois Group as $S_4$
- How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
- Galois ring extension

Let $\sigma$ be an automophism of $F$.

Let $S$ be a transcendence basis of $A$ over $F$.

There exists a unique automorphism $\tau$ of $F(S)$ such that $\tau|F = \sigma$ and $\tau(x) = x$ for every $x \in S$.

Since $A$ is an algebraic closure of $F(S)$, there exists an automorphism $\rho$ of $A$ extending $\tau$. Then $\rho$ extends $\sigma$.

- An $r\times r$ submatrix of independent rows and independent columns is invertible (Michael Artin's book).
- Importance of Constructible functions
- Finite field question involving the trace and a permutation.
- Finding $a_n$ for very large $n$ where $a_n = a_{n-1} + a_{n-2} + a_{n-3} + 2^{n-3} $
- Infinite product of recursive sequence
- Understanding the derivative as a linear transformation
- Two styles of semantics for a first-order language: what's to choose?
- Why is $|x|$ not differentiable at $x=0$?
- finding the real values of $x$ such that : $x=\sqrt{2+\sqrt{2-\sqrt{2+x}}}$
- The epsilon-delta definition of continuity
- Dense subsets in tensor products of Banach spaces
- Compute the mean of $(1 + x)^{-1}$
- What is the rank of the cofactor matrix of a given matrix?
- What is the cardinality of the set of all sequences in $\mathbb{R}$ converging to a real number?
- Find the LCM of 3 numbers given HCF of each 2.