Newbetuts
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New posts in field-theory
Why doesn't stuff hold in characteristic non-zero?
abstract-algebra
field-theory
Why is the difference of distinct roots of irreducible $f(x)\in\mathbb{Q}[x]$ never rational?
abstract-algebra
polynomials
field-theory
If $E/F$ is algebraic and every $f\in F[X]$ has a root in $E$, why is $E$ algebraically closed? [duplicate]
abstract-algebra
field-theory
A finite field cannot be an ordered field.
abstract-algebra
field-theory
ordered-fields
No extension to complex numbers?
field-theory
complex-numbers
Every finite group is isomorphic to some Galois group for some finite normal extension of some field.
finite-groups
field-theory
galois-theory
Algebraic extensions are isomorphic if the same polynomials have roots
abstract-algebra
field-theory
model-theory
axiom-of-choice
field generated by a set
abstract-algebra
field-theory
Irreducibility of $x^{n}+x+1$
polynomials
field-theory
galois-theory
factoring
Galois Group of $x^{4}+7$
abstract-algebra
field-theory
galois-theory
splitting-field
show that if $K$ is a field then $K[x]$ is principal [duplicate]
abstract-algebra
ring-theory
field-theory
How to convert $\Bbb Q(\sqrt 2,\sqrt 3)$ to $\Bbb Q(\alpha)?$
field-theory
extension-field
Finding basis of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ over $\mathbb{Q}$
abstract-algebra
field-theory
extension-field
Irreducible polynomial in field extension
polynomials
field-theory
extension-field
irreducible-polynomials
Prove that a polynomial is irreducible or the field contains a $p$th root
abstract-algebra
field-theory
irreducible-polynomials
positive-characteristic
Do people ever study non-commutative fields?
field-theory
noncommutative-algebra
Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$ [duplicate]
field-theory
galois-theory
extension-field
roots-of-unity
cyclotomic-fields
When, and by whom, was "$\mathbb{C}$ is algebraically closed" dubbed the "fundamental theorem of algebra"?
abstract-algebra
reference-request
field-theory
math-history
Addition law of the tilt $K^\flat$ of a field $K$
field-theory
modular-arithmetic
Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?
field-theory
finite-fields
extension-field
irreducible-polynomials
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