New posts in field-theory

Field extensions of finite degree and primitive elements

abstract-algebra field-theory extension-field minimal-polynomials

Number fields with all degrees equal to a power of three

Is there only one way to make $\mathbb R^2$ a field?

Which cyclotomic fields are different?

field-theory extension-field cyclotomic-fields

A finite field extension of $\mathbb R$ is either $\mathbb R$ or isomorphic to $\mathbb C$

abstract-algebra field-theory extension-field

Are distinct prime ideals in a ring always coprime? If not, then when are they?

ring-theory algebraic-number-theory field-theory ideals

Norm of element $\alpha$ equal to absolute norm of principal ideal $(\alpha)$

abstract-algebra field-theory algebraic-number-theory ideals

Show that $x^4-x^2+1$ is irreducible over $\mathbb{Q}$

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

Irreducibility of $x^{2n}+x^n+1$

field-theory finite-fields irreducible-polynomials

Proof Verification : Prove -(-a)=a using only ordered field axioms [duplicate]

analysis proof-verification field-theory

What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?

Non-trivial example of algebraically closed fields

abstract-algebra field-theory

Is $\mathbb Q_r$ algebraically isomorphic to $\mathbb Q_s$ while r and s denote different primes?

number-theory field-theory p-adic-number-theory

Why is the product of all units of a finite field equal to $-1$?

field-theory finite-fields

Intermediate fields between $\mathbb{Z}_2 (\sqrt{x},\sqrt{y})$ and $\mathbb{Z}_2 (x,y)$

abstract-algebra field-theory

Galois group of an irreducible polynomial

abstract-algebra group-theory polynomials field-theory galois-theory

Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$

abstract-algebra field-theory

Why isn't the zero ring the field with one element?

algebraic-geometry field-theory finite-fields

Examples of fields of characteristic 0?

abstract-algebra field-theory

The real numbers are a field extension of the rationals?

field-theory extension-field