New posts in field-theory

Why doesn't stuff hold in characteristic non-zero?

Why is the difference of distinct roots of irreducible $f(x)\in\mathbb{Q}[x]$ never rational?

If $E/F$ is algebraic and every $f\in F[X]$ has a root in $E$, why is $E$ algebraically closed? [duplicate]

A finite field cannot be an ordered field.

No extension to complex numbers?

Every finite group is isomorphic to some Galois group for some finite normal extension of some field.

Algebraic extensions are isomorphic if the same polynomials have roots

field generated by a set

Irreducibility of $x^{n}+x+1$

Galois Group of $x^{4}+7$

show that if $K$ is a field then $K[x]$ is principal [duplicate]

How to convert $\Bbb Q(\sqrt 2,\sqrt 3)$ to $\Bbb Q(\alpha)?$

Finding basis of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ over $\mathbb{Q}$

Irreducible polynomial in field extension

Prove that a polynomial is irreducible or the field contains a $p$th root

Do people ever study non-commutative fields?

Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$ [duplicate]

When, and by whom, was "$\mathbb{C}$ is algebraically closed" dubbed the "fundamental theorem of algebra"?

Addition law of the tilt $K^\flat$ of a field $K$

Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?