New posts in irreducible-polynomials

Irreducibility of $X^n-a$

polynomials irreducible-polynomials

Irreducible homogeneous polynomials of arbitrary degree

algebraic-geometry polynomials irreducible-polynomials

Is $f(X)=(2+i)X^4+5X^2-3i$ irreducible over $\mathbb{Z}[i]$?

abstract-algebra polynomials irreducible-polynomials

How to prove that the polynomial $x^n+x^{n-1} +⋯+x^2+x−1$ is irreducible over $ \mathbb Q$?

polynomials irreducible-polynomials

Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $

abstract-algebra polynomials ring-theory irreducible-polynomials

Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$

abstract-algebra polynomials irreducible-polynomials

Irreducibility check for polynomials not satisfying Eisenstein Criterion.

abstract-algebra ring-theory irreducible-polynomials

Show that $x^4 + 8$ is irreducible over Z

abstract-algebra irreducible-polynomials

Prove $f(x)=x^8-24 x^6+144 x^4-288 x^2+144$ is irreducible over $\mathbb{Q}$

irreducible-polynomials minimal-polynomials splitting-field

Irreducibility criteria for polynomials with several variables.

abstract-algebra ring-theory irreducible-polynomials polynomial-rings

Determine splitting field $K$ over $\mathbb{Q}$ of the polynomial $x^3 - 2$

field-theory irreducible-polynomials roots-of-unity splitting-field

Proving irreducibility of $x^6-72$

abstract-algebra irreducible-polynomials

Prove that a polynomial is irreducible

field-theory irreducible-polynomials

$f,g$ be irr poly of degree $m$ and $n$. Show that if $\alpha$ is a root of $f$ in some extension of $F$, then $g$ is ireducible in $F(\alpha)[x]$

abstract-algebra field-theory extension-field irreducible-polynomials

Reducibility over $\mathbb{Z}_2$?

abstract-algebra polynomials irreducible-polynomials

Explaining Newton Polygon for proving irreducibility of polynomial in $\mathbb{Z}[x]$ in elementary way

polynomials intuition irreducible-polynomials

How to choose correct strategy for irreducibility testing in $\mathbb{Z}[X]$?

abstract-algebra soft-question irreducible-polynomials

Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$ [duplicate]

abstract-algebra polynomials finite-fields irreducible-polynomials

Irreducible polynomial in field extension

polynomials field-theory extension-field irreducible-polynomials

Prove that a polynomial is irreducible or the field contains a $p$th root

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