New posts in field-theory

Are $\mathbb{R}[X] / (X^2 +1)$ and $\mathbb{C}$ homeomorphic?

general-topology complex-numbers field-theory quotient-spaces

Can I embed $\Bbb{C}(x)$ into $\Bbb{C}$?

Is the Pythagorean closure of $\mathbb Q$ equal to the field of constructible numbers?

$\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$

abstract-algebra polynomials field-theory extension-field

extension of automorphism of field to algebraically closed field

field-theory galois-theory

Does $t^{p-1}$ have an antiderivative in $\Bbb F_q(t)$?

abstract-algebra field-theory finite-fields rational-functions function-fields

What exactly is the fixed field of the map $t\mapsto t+1$ in $k(t)$?

functions polynomials field-theory

Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field [duplicate]

abstract-algebra field-theory

Zeros of polynomial over an infinite field

The exponential extension of $\mathbb{Q}$ is a proper subset of $\mathbb{C}$?

number-theory field-theory exponential-function extension-field

Why should I consider the components $j^2$ and $k^2$ to be $=-1$ in the search for quaternions?

abstract-algebra group-theory field-theory quaternions

The set of algebraic numbers is a field.

abstract-algebra field-theory

If $(F:E)<\infty$, is it always true that $\operatorname{Aut}(F/E)\leq(F:E)?$

Prove that the number of $\alpha\in\mathbb{F}_{27}$ such that $|A_\alpha|=26 $ equals 12.

field-theory finite-fields

Is it actually incorrect to say $x/1 = x$?

abstract-algebra field-theory

Why any field is a principal ideal domain?

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

A field of order $32$

abstract-algebra field-theory finite-fields

How to show every field is a Euclidean Domain.

abstract-algebra field-theory integral-domain euclidean-algorithm

Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.

abstract-algebra ring-theory field-theory self-learning ideals

A question regarding the definition of Galois group

abstract-algebra group-theory field-theory galois-theory