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New posts in extension-field
Do extension fields always belong to a bigger field?
abstract-algebra
field-theory
extension-field
If the Galois group is $S_3$, can the extension be realized as the splitting field of a cubic?
field-theory
galois-theory
extension-field
splitting-field
Embedding Fields in Matrix Rings
abstract-algebra
field-theory
extension-field
Finiteness of the Algebraic Closure
abstract-algebra
field-theory
extension-field
A basis for $k(X)$ regarded as a vector space over $k$
linear-algebra
vector-spaces
extension-field
$f(x) $ be the minimal polynomial of $a$ (algebraic element) over $\mathbb Q$ , let $b=f'(a) \in \mathbb Q(a)$ , then is $\mathbb Q(a)=\mathbb Q(b)$?
ring-theory
field-theory
extension-field
minimal-polynomials
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$ [duplicate]
field-theory
galois-theory
roots
extension-field
Does every infinite field contain a countably infinite subfield?
abstract-algebra
field-theory
extension-field
Let $F$ be a field, and $K$ a field extension of $F$. Prove that $[K:F] = 1$ iff $K=F$.
abstract-algebra
extension-field
Is it possible for an irreducible polynomial with rational coefficients to have three zeros in an arithmetic progression?
abstract-algebra
galois-theory
extension-field
irreducible-polynomials
Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
abstract-algebra
field-theory
extension-field
Why there is much interest in the study of $\operatorname{Gal}\left(\overline{\mathbb Q}/\mathbb Q\right)$?
algebraic-geometry
soft-question
galois-theory
extension-field
big-picture
Fundamental question about field extensions
abstract-algebra
ring-theory
commutative-algebra
field-theory
extension-field
localization in the D + M construction
abstract-algebra
commutative-algebra
extension-field
localization
integral-extensions
Ring Inside an Algebraic Field Extension [duplicate]
abstract-algebra
ring-theory
extension-field
Order of field extension
abstract-algebra
field-theory
extension-field
splitting-field
Similar matrices and field extensions
linear-algebra
abstract-algebra
matrices
extension-field
Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.
abstract-algebra
field-theory
extension-field
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