New posts in field-theory

Embed finite field in algebraic closed field

abstract-algebra field-theory finite-fields

Is $\operatorname{Gal}(\mathbb{Q}_p^{un})\cong \hat{\mathbb{Z}}$?

number-theory algebraic-geometry field-theory galois-theory

How can I know how many real roots this polynomial has?

abstract-algebra polynomials field-theory

Question About Notation In Field Theory $F(x)$ vs. $F[x]$

abstract-algebra field-theory notation

$|\operatorname{Aut}(K/F)| \leq [K:F]_s$ holds in general?

abstract-algebra field-theory galois-theory extension-field automorphism-group

Determine the Galois Group of $(x^2-2)(x^2-3)(x^2-5)$

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

Is $\Bbb Q(\sqrt 2, e)$ a simple extension of $\Bbb Q$?

abstract-algebra field-theory extension-field transcendence-theory

What is meant by a mixed characteristic field?

abstract-algebra field-theory

Is every discrete absolute value non-archimedean?

field-theory valuation-theory

Dimension of an algebraic closure as a vector space over its base field.

What is the difference between an axiom and a definition?

field-theory definition axioms

Prove that the tensor product of non algebraic extensions is not a field

abstract-algebra field-theory galois-theory extension-field tensor-products

Integral closure of p-adic integers in maximal unramified extension

number-theory commutative-algebra algebraic-number-theory field-theory p-adic-number-theory

Splitting field implies Galois extension

abstract-algebra field-theory galois-theory

What kinds of non-zero characteristic fields exist?

Minimal polynomial of $\zeta+\zeta^{-1}$

abstract-algebra field-theory galois-theory cyclotomic-polynomials

Is there a 'conjugation' on every algebraically closed field?

abstract-algebra field-theory

Example of a nontransitive action of $\operatorname{Aut}(K/\mathbb Q)$ on the roots in $K$ of an irreducible polynomial.

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

Source to learn Galois Theory

abstract-algebra reference-request field-theory galois-theory book-recommendation

Unramified primes of splitting field

abstract-algebra polynomials commutative-algebra field-theory algebraic-number-theory