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New posts in extension-field
$|\operatorname{Aut}(K/F)| \leq [K:F]_s$ holds in general?
abstract-algebra
field-theory
galois-theory
extension-field
automorphism-group
Galois: Why does $\{1,f,f^2\}$ correspond to $\mathbb{Q}(\omega)$?
galois-theory
extension-field
galois-extensions
How do extension fields implement $>, <$ comparisons?
abstract-algebra
extension-field
ordered-fields
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
$L$ is an extension of $K$, if $L$ is a $K$-algebra
abstract-algebra
extension-field
Prove that the tensor product of non algebraic extensions is not a field
abstract-algebra
field-theory
galois-theory
extension-field
tensor-products
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
Can we always find field extensions of a given number field and a given degree?
field-theory
extension-field
Why is $\mathbb{Q}(\operatorname{exp}(\frac{2\pi i}{5}))$ a field extension of degree four not five?
abstract-algebra
field-theory
extension-field
minimal-polynomials
What is the intuition behind defining this isomorphism?
abstract-algebra
ring-theory
field-theory
finite-fields
extension-field
Dirichlet characters and quadratic fields
number-theory
algebraic-number-theory
extension-field
characters
If $L\mid K$ is a finite extension of fields then K is perfect iff L is perfect
abstract-algebra
algebraic-geometry
field-theory
extension-field
Why is the extension $k(x,\sqrt{1-x^2})/k$ purely transcendental?
abstract-algebra
algebraic-geometry
field-theory
extension-field
algebraic-curves
Set of elements in $K$ that are purely inseparable over $F$ is a subfield
abstract-algebra
field-theory
extension-field
Finding a Galois extension of $\Bbb Q$ of degree $3$
abstract-algebra
field-theory
galois-theory
extension-field
Show $Gal(E/\mathbb{Q})\cong \mathbb{\mathbb{Z_2\times Z_2}}$
abstract-algebra
galois-theory
extension-field
Is the subextension of a purely transcendental extension purely transcendental over the base field?
galois-theory
extension-field
transcendence-degree
Why is the degree of a rational map of projective curves equal to the degree of the homogeneous polynomials?
algebraic-geometry
extension-field
algebraic-curves
function-fields
If a real number can be expressed in terms of complex solutions of cubic equations, can it be expressed in terms of real solutions of cubic equations?
complex-numbers
field-theory
algebraic-number-theory
extension-field
cubics
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