New posts in field-theory

Counting centralizers of a matrix over a finite field with a particular minimal polynomial

abstract-algebra matrices group-theory field-theory

Do groups, rings and fields have practical applications in CS? If so, what are some?

group-theory ring-theory soft-question field-theory big-picture

Why is a finite integral domain always field?

abstract-algebra ring-theory field-theory integral-domain finite-rings

Continuity of the roots of a polynomial in terms of its coefficients

analysis polynomials field-theory roots

Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field

field-theory

Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?

abstract-algebra field-theory

How to solve fifth-degree equations by elliptic functions?

polynomials field-theory galois-theory elliptic-functions

How to find the Galois group of a polynomial?

abstract-algebra field-theory galois-theory

Wild automorphisms of the complex numbers

complex-numbers field-theory

How to prove that the sum and product of two algebraic numbers is algebraic? [duplicate]

abstract-algebra field-theory

Irreducible cyclotomic polynomial

field-theory galois-theory finite-fields

Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?

abstract-algebra field-theory

Example of infinite field of characteristic $p\neq 0$

abstract-algebra field-theory examples-counterexamples

Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$

abstract-algebra polynomials field-theory galois-theory finite-fields

Is an automorphism of the field of real numbers the identity map?

abstract-algebra field-theory real-numbers

Irreducible polynomial which is reducible modulo every prime

abstract-algebra polynomials field-theory finite-fields irreducible-polynomials

How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?

positive-characteristic abstract-algebra polynomials field-theory irreducible-polynomials

Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?

linear-algebra vector-spaces field-theory

Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.

abstract-algebra field-theory extension-field

The square roots of different primes are linearly independent over the field of rationals

abstract-algebra number-theory prime-numbers field-theory