Newbetuts
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New posts in field-theory
Simplify $\mathbb{Q}(\pi^3+\pi^2, \pi^8+\pi^5)$
elementary-number-theory
field-theory
transcendental-numbers
Showing $[K(x):K(\frac{x^5}{1+x})]=5$?
field-theory
extension-field
transcendence-degree
An element is integral iff its minimal polynomial has integral coefficients.
field-theory
algebraic-number-theory
Finite Field Extensions and the Sum of the Elements in Proper Subextensions (Follow-Up Question)
field-theory
finite-fields
Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
abstract-algebra
polynomials
field-theory
Intersection of field extensions
abstract-algebra
field-theory
Extension of isomorphism of fields
field-theory
extension-field
automorphism-group
Is there a subfield of $\mathbb{R}$ that is a proper elementary extension of $\mathbb{Q}$?
field-theory
model-theory
Polynomial rings -- Inherited properties from coefficient ring
abstract-algebra
polynomials
ring-theory
field-theory
A finite field extension $K\supset\mathbb Q$ contains finitely many roots of unity
abstract-algebra
field-theory
roots-of-unity
Computing a uniformizer in a totally ramified extension of $\mathbb{Q}_p$.
field-theory
algebraic-number-theory
p-adic-number-theory
local-field
ramification
Infinite number of intermediate fields between K(u,v) and K
abstract-algebra
field-theory
In a field extension, if each element's degree is bounded uniformly by $n$, is the extension finite?
abstract-algebra
field-theory
extension-field
Suppose $K/F$ is a Galois extension of degree $p^m$. Then there is a chain of extensions $F \subseteq F_1 \subseteq \cdots F_m = K$ each of degree $p$
abstract-algebra
group-theory
field-theory
galois-theory
sylow-theory
On the unicity of splitting field
field-theory
extension-field
Generic Element of Compositum of Two Fields [duplicate]
field-theory
extension-field
tensor-products
Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
abstract-algebra
field-theory
galois-theory
Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?
abstract-algebra
field-theory
extension-field
radicals
axiom-of-choice
$f$ is irreducible $\iff$ $G$ act transitively on the roots
field-theory
galois-theory
How is the degree of the minimal polynomial related to the degree of a field extension?
field-theory
galois-theory
extension-field
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