New posts in field-theory

Does every infinite field contain a countably infinite subfield?

abstract-algebra field-theory extension-field

Is a field determined by its family of general linear groups?

linear-algebra abstract-algebra group-theory field-theory

Trigonometric diophantine equation $8\sin^2\left(\frac{(k+1)\pi}{n}\right)=n\sin\left(\frac{2\pi}{n}\right)$

number-theory trigonometry field-theory diophantine-equations

Quadratic extensions in characteristic $2$

Finding the minimal polynomial of $\sqrt 2 + \sqrt[3] 2$ over $\mathbb Q$.

polynomials field-theory minimal-polynomials

Why is $\mathbb{Q}(t,\sqrt{t^3-t})$ not a purely transcendental extension of $\mathbb{Q}$?

abstract-algebra field-theory

Basis of primitive nth Roots in a Cyclotomic Extension?

linear-algebra field-theory

Axiomatic characterization of the rational numbers

logic field-theory axioms rational-numbers

Generalisation of integers for infinite length?

field-theory terminology infinite-groups

Why isn't the inverse of the function $x\mapsto x+\sin(x)$ expressible in terms of "the functions one finds on a calculator"?

functions field-theory galois-theory

Non-principal ideal in $K[x,y]$? [duplicate]

abstract-algebra ring-theory field-theory principal-ideal-domains

Why $\mathbb{C}(f(t),g(t))=\mathbb{C}(t)$ implies that $\gcd(f(t)-a,g(t)-b)=t-c$, for some $a,b,c \in \mathbb{C}$?

polynomials commutative-algebra field-theory gcd-and-lcm

Rigidity of the category of fields

category-theory field-theory

Showing that a finite commutative ring with more than one element and no zero divisors has an identity. [duplicate]

abstract-algebra ring-theory field-theory

Sum of irrational numbers, a basic algebra problem

abstract-algebra number-theory field-theory

A finite field extension that is not simple

abstract-algebra ring-theory field-theory

Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm) [duplicate]

abstract-algebra polynomials field-theory

Is it true in an arbitrary field that $-1$ is a sum of two squares iff it is a sum of three squares?

If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field. [duplicate]

commutative-algebra ring-theory field-theory modules

Proving that a polynomial is not solvable by radicals.

abstract-algebra polynomials field-theory galois-theory