New posts in extension-field

If $K$ is algebraically closed, is the fixed field of an involution real-closed?

field-theory algebraic-number-theory extension-field

Deduce the degree of the extension $[\mathbb C:K]$ is countable and not finite

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

If $F/L$ is normal and $L/K$ is purely inseparable, then $F/K$ is normal

abstract-algebra field-theory extension-field

Polynomials $P(x)\in k[x]$ satisfying condition $P(x^2)=P(-x)P(x)$

combinatorics polynomials field-theory extension-field functional-equations

Is following a normal field extension?

abstract-algebra extension-field

Philosophy of simple field extensions

abstract-algebra polynomials extension-field

Basis of extension of scalars

abstract-algebra extension-field tensor-products

Can we construct $\Bbb C$ without first identifying $\Bbb R$?

abstract-algebra field-theory extension-field

Fields and cubic extensions

field-theory extension-field

Isomorphism between $\Bbb R$ and $\Bbb R(X)$?

abstract-algebra field-theory extension-field

This tower of fields is being ridiculous

abstract-algebra field-theory extension-field fake-proofs

Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.

abstract-algebra polynomials field-theory extension-field

Simple extension of $\mathbb{Q} (\sqrt[4]{2},i)$

abstract-algebra field-theory galois-theory extension-field irreducible-polynomials

How to find the degree of a field extension

abstract-algebra field-theory definition extension-field

Minimum polynomial of $\sqrt{2} + \sqrt[3]{5}$ above $\mathbb{Q}$ (and a generalization)

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

Definition of *pure* transcendental extension

definition extension-field

Algebraic closure of $k((t))$

abstract-algebra extension-field class-field-theory

How to show that $\sqrt{3 - \sqrt{2}} \notin \mathbb{Q}(\sqrt{3 + \sqrt{2}})$ [duplicate]

abstract-algebra galois-theory extension-field radicals nested-radicals

Proof that $K\otimes_F L$ is not noetherian

commutative-algebra extension-field

Algebraic extension of $\Bbb Q$ with exactly one extension of given degree $n$

abstract-algebra field-theory extension-field