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Eisenstein Criterion
abstract-algebra
polynomials
irreducible-polynomials
Discuss $\mathbb R[X]/(aX^2 +bX + c)$ in terms of $\Delta = b^2-4ac$
abstract-algebra
polynomials
ring-theory
irreducible-polynomials
quotient-group
Polynomial irreducible - maximal ideal
abstract-algebra
field-theory
proof-verification
ideals
irreducible-polynomials
$x^p -x-c$ is irreducible over a field of characteristic $p$ if it has no root in the field
abstract-algebra
polynomials
field-theory
irreducible-polynomials
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
abstract-algebra
polynomials
ring-theory
factoring
irreducible-polynomials
Homogenous polynomials in $K[X,Y]$ split into linear factors [duplicate]
abstract-algebra
algebraic-geometry
polynomials
commutative-algebra
irreducible-polynomials
Check the proof of:$x^2+1$ is irreducible over $\Bbb Q$
polynomials
irreducible-polynomials
When is $X_1^{a_1} \cdots X_n^{a_n}-1$ irreducible?
abstract-algebra
polynomials
commutative-algebra
irreducible-polynomials
Minimal polynomial of product, sum, etc., of two algebraic numbers
polynomials
algebraic-number-theory
irreducible-polynomials
minimal-polynomials
Reducibility of $x^3+nx+1$ over $ \Bbb Z$
algebra-precalculus
diophantine-equations
irreducible-polynomials
integers
How prove $P(x)=\sum_{k=0}^{n}(2k+1)x^k$ is irreducible over $\mathbb{Q}$
polynomials
irreducible-polynomials
Construction of addition and multiplication table for GF(4)
finite-fields
irreducible-polynomials
Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$
number-theory
irreducible-polynomials
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$ [duplicate]
abstract-algebra
algebraic-number-theory
extension-field
irreducible-polynomials
Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?
abstract-algebra
polynomials
finite-fields
irreducible-polynomials
Every irreducible polynomial f over perfect field F is separable
abstract-algebra
polynomials
field-theory
irreducible-polynomials
Polynomial with a root modulo every prime but not in $\mathbb{Q}$. [duplicate]
abstract-algebra
number-theory
irreducible-polynomials
How to check that a cubic polynomial is irreducible?
abstract-algebra
polynomials
finite-fields
irreducible-polynomials
Why are $i$ and $-i$ "more indistinguishable" than $\sqrt{2}$ and $-\sqrt{2}$?
abstract-algebra
complex-numbers
field-theory
extension-field
irreducible-polynomials
Irreducibility of $p^{n-1}X^n+pX+1$ over $\mathbb{Q}$ [duplicate]
number-theory
polynomials
prime-numbers
irreducible-polynomials
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