Newbetuts

Without using Dirichlet's theorem, show that there are infinitely primes congruent to $a$ mod n if $a^2\equiv 1\,(\!\bmod\; n)$ [duplicate]

Two finite fields with the same number of elements are isomorphic

Prove a certain cyclic extension with prime power order is simple

Basis for $\mathbb Q (\sqrt2 , \sqrt3 )$ over $\mathbb Q$

Prove that $T$ has a cyclic vector iff its minimal and characteristic polynomials are the same

the discriminant of the cyclotomic $\Phi_p(x)$

What is a field?

$\mathbb R^3$ is not a field

Are all finite fields isomorphic to $\mathbb{F}_p$?

Is $\mathbb{R}$ an algebraic extension of some proper subfield?

Show that $\mathbb{Q}(\sqrt{2 +\sqrt{2}})$ is a cyclic quartic field i.e. is a galois extension of degree 4 with cyclic galois group [duplicate]

Are $\Bbb R$ and $\Bbb C$ the only connected, locally compact fields?

$\mathbb{C}(f,g)=\mathbb{C}(t)$ and $(f'(t),g'(t)) \neq 0$, but $\mathbb{C}[f,g]\subsetneq \mathbb{C}[t]$

Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$

Numbers whose powers are almost integers

A slick proof that a field which is finitely generated as a ring is finite

Fields the closure of which is $\mathbb{C}$

New posts in field-theory

Lüroth's Theorem

Construct algebraic closure of $\mathbb{Q}$

Radical extension

Without using Dirichlet's theorem, show that there are infinitely primes congruent to $a$ mod n if $a^2\equiv 1\,(\!\bmod\; n)$ [duplicate]

Two finite fields with the same number of elements are isomorphic

Prove a certain cyclic extension with prime power order is simple

Basis for $\mathbb Q (\sqrt2 , \sqrt3 )$ over $\mathbb Q$

Prove that $T$ has a cyclic vector iff its minimal and characteristic polynomials are the same

the discriminant of the cyclotomic $\Phi_p(x)$

What is a field?

$\mathbb R^3$ is not a field

Are all finite fields isomorphic to $\mathbb{F}_p$?

Is $\mathbb{R}$ an algebraic extension of some proper subfield?

Show that $\mathbb{Q}(\sqrt{2 +\sqrt{2}})$ is a cyclic quartic field i.e. is a galois extension of degree 4 with cyclic galois group [duplicate]

Are $\Bbb R$ and $\Bbb C$ the only connected, locally compact fields?

$\mathbb{C}(f,g)=\mathbb{C}(t)$ and $(f'(t),g'(t)) \neq 0$, but $\mathbb{C}[f,g]\subsetneq \mathbb{C}[t]$

Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$

Numbers whose powers are almost integers

A slick proof that a field which is finitely generated as a ring is finite

Fields the closure of which is $\mathbb{C}$