Newbetuts
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New posts in field-theory
Splitting field of $x^{n}-1$ over $\mathbb{Q}$
abstract-algebra
field-theory
galois-theory
Irrationality of $(a_1+\sqrt{b_1})(a_2+\sqrt{b_2})$
abstract-algebra
ring-theory
field-theory
roots
irrational-numbers
Determining the Galois group of a cubic without using discriminant
abstract-algebra
group-theory
field-theory
galois-theory
Complete ordered field
field-theory
ordered-fields
Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
field-theory
galois-theory
Find an example of a non-surjective field endomorphism
abstract-algebra
field-theory
Does $\mathbb{F}_p((X))$ has only finitely many extension of a given degree?
number-theory
field-theory
algebraic-number-theory
extension-field
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
abstract-algebra
polynomials
field-theory
finite-fields
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
abstract-algebra
polynomials
field-theory
irreducible-polynomials
Show that an algebraically closed field must be infinite.
abstract-algebra
field-theory
Intermediate fields of a finite field extension that is not separable
abstract-algebra
field-theory
finite-fields
extension-field
Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8 [duplicate]
abstract-algebra
galois-theory
field-theory
Are there number systems corresponding to higher cardinalities than the real numbers?
field-theory
cardinals
model-theory
infinity
How can a field have a finite characteristic $p$, given that a field has no zero divisors?
abstract-algebra
field-theory
positive-characteristic
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?
abstract-algebra
field-theory
galois-theory
extension-field
Finding Galois group of $x^6 - 3x^3 + 2$
field-theory
galois-theory
extension-field
Every finite extension of a finite field is separable
abstract-algebra
field-theory
Does there exist a pair of infinite fields, the additive group of one isomorphic to the multiplicative group of the other?
field-theory
group-isomorphism
positive-characteristic
what is a "dévissage" argument?
algebraic-geometry
field-theory
terminology
algebraic-number-theory
arithmetic-geometry
Example of a complete, non-archimedean ordered field
real-analysis
field-theory
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