New posts in field-theory

Given a proper field extension $L/K$, can we have $L\cong K$? [duplicate]

abstract-algebra field-theory extension-field ring-isomorphism

galois group of finite field [duplicate]

field-theory galois-theory extension-field galois-extensions

What is the degree of a real closure of an ordered field?

field-theory cardinals model-theory extension-field ordered-fields

Determine the degree of the splitting field for $f(x)=x^{15}-1$.

abstract-algebra field-theory finite-fields extension-field cyclotomic-polynomials

A *finite* first order theory whose finite models are exactly the $\Bbb F_p$?

logic field-theory finite-fields model-theory first-order-logic

Field Norm Surjective for Finite Extensions of $\mathbb{F}_{p^k}$

field-theory galois-theory finite-fields

If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$

abstract-algebra field-theory extension-field

Quadratic subfield of cyclotomic field [duplicate]

abstract-algebra field-theory galois-theory cyclic-groups roots-of-unity

Polynomial irreducible - maximal ideal

abstract-algebra field-theory proof-verification ideals irreducible-polynomials

Perfect closure is perfect

abstract-algebra field-theory

Question about fields and quotients of polynomial rings

abstract-algebra commutative-algebra field-theory

Elliptic curve over algebraically closed field of characteristic $0$ has a non-torsion point

number-theory algebraic-geometry field-theory elliptic-curves abelian-varieties

Solving for the functional shifts and its inverse

calculus field-theory

$x^p -x-c$ is irreducible over a field of characteristic $p$ if it has no root in the field

abstract-algebra polynomials field-theory irreducible-polynomials

(The number of) embeddings of an algebraic extension of $\mathbb{Q}$ into $\mathbb{C}$

algebraic-number-theory field-theory

"Place" vs. "Prime" in a number field.

number-theory field-theory algebraic-number-theory

Elementary proof of $\mathbb{Q}(\zeta_n)\cap \mathbb{Q}(\zeta_m)=\mathbb{Q}$ when $\gcd(n,m)=1$.

abstract-algebra algebraic-number-theory field-theory

Find intermediate fields of $\mathbb{Q}(\sqrt[3]{2}, \sqrt{3},i) \, | \, \mathbb{Q}(i)$

abstract-algebra field-theory galois-theory extension-field

Understanding that $\mathbb{R}(X^2 + Y^2, XY)(x) \supset \mathbb{R}(Y)$?

abstract-algebra field-theory galois-theory extension-field

$K$ is a splitting field $\iff$ any irreducible polynomial with a root in $K$ splits completely over $K$.

abstract-algebra field-theory extension-field