New posts in field-theory

Elementary proof that there is no field with 6 elements

abstract-algebra field-theory finite-fields alternative-proof

Can we always find a primitive element that is a square?

abstract-algebra field-theory extension-field

Are the real numbers a nontrivial simple extension of another field?

A problem on field extension

A finite extension with finitely many intermediate fields is simple

General way to determine $\mathbb{Q}(\gamma) = \mathbb{Q}(\alpha,\beta)$ given $\alpha$ and $\beta$

abstract-algebra field-theory extension-field

Irreducible implies minimal polynomial?

abstract-algebra field-theory galois-theory

Why is $\mathbb{C}_p$ isomorphic to $\mathbb{C}$?

abstract-algebra field-theory valuation-theory

Good undergraduate level book on Cyclotomic fields

reference-request algebraic-number-theory field-theory

Elements of $GL_{2}(\mathbb{Z})$ of finite order

abstract-algebra matrices field-theory linear-groups

Is a bivariate function that is a polynomial function with respect to each variable necessarily a bivariate polynomial?

polynomials field-theory

The Galois group is $\mathbb{Z_{4}}$ if and only if $\frac{\alpha}{\beta}-\frac{\beta}{\alpha}\in\mathbb{Q}$

abstract-algebra field-theory galois-theory

Characterization of a subfield $K \varsubsetneq \mathbb {C}$ and $x\in \mathbb{R}$

abstract-algebra field-theory

Why is this extension of Galois?

field-theory galois-theory

Trace as Bilinear form on a field extension

field-theory galois-theory bilinear-form

Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible

abstract-algebra field-theory

Show that $f(x) = x^p -x -1 \in \Bbb{F}_p[x]$ is irreducible over $\Bbb{F}_p$ for every $p$.

abstract-algebra field-theory finite-fields positive-characteristic

Infinite direct product of fields.

linear-algebra abstract-algebra vector-spaces field-theory

Why any homomorphism between fields over $\mathbb Q$ fixes $\mathbb Q$ pointwise?

abstract-algebra field-theory galois-theory

Galois Field Fourier Transform

field-theory finite-fields coding-theory