New posts in field-theory

Finitely generated field extensions

abstract-algebra field-theory

Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension

abstract-algebra field-theory extension-field

Algebraic extension of perfect field in which every polynomial has a root is algebraically closed

field-theory extension-field

Separable field extensions *without* using embeddings or automorphisms

abstract-algebra reference-request field-theory extension-field

find total number of maximal ideals in $\mathbb{Q}[x]/\langle x^4-1\rangle$.

abstract-algebra proof-verification ring-theory field-theory

Field extension of composite degree has a non-trivial sub-extension

field-theory galois-theory

Unramified extension is normal if it has normal residue class extension

field-theory p-adic-number-theory

A formula for the roots of a solvable polynomial

abstract-algebra field-theory galois-theory

What is the algebraic closure of $\mathbb F_q$?

abstract-algebra field-theory finite-fields

Splitting field of $x^6+x^3+1$ over $\mathbb{Q}$

abstract-algebra field-theory

Why aren't there any coproducts in the category of $\bf{Fields}$?

field-theory category-theory

If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?

polynomials field-theory extension-field

Applications of additive version of Hilbert's theorem 90

number-theory field-theory algebraic-number-theory galois-theory galois-cohomology

Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.

field-theory extension-field

The Noether-Deuring Theorem

field-theory representation-theory modules

Set of elements of degree $2^n$ over a base field is itself a field

abstract-algebra field-theory extension-field

Is the sum of an algebraic and transcendental complex number transcendental?

abstract-algebra field-theory galois-theory transcendental-numbers

Irreducibility of cyclotomic polynomials over number fields

abstract-algebra field-theory algebraic-number-theory irreducible-polynomials cyclotomic-polynomials

What is the condition for a field to make the degree of its algebraic closure over it infinite?

abstract-algebra field-theory galois-theory

Find all irreducible polynomials of degrees 1,2 and 4 over $\mathbb{F_2}$.

abstract-algebra ring-theory field-theory