$f(x) \in F[x]$ is irreducible over $F$ if $f(x) = g(x)h(x)$ implies that $g(x) \in F$ or $h(x) \in F$ where $F$ is a field.
73344
Definition of irreducible polynomial via the units of an integral domain.
146887
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
48093
Irreducible polynomial in field extension
143107
Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
158282
Finite order of an element $f(g)$ of a homomorphism $f$
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
104757
If $f \circ g$ is surjective, then f is surjective
12166
How many irreducible polynomials of degree $n$ exist over $\mathbb{F}_p$?
72251
$g\circ f$ is Surjective and $g$ is Injective then Prove that $f$ is surjective
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
78540
Every irreducible polynomial f over perfect field F is separable
102422
Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
56413
$f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
19968
Describe all $p^{n}$ (in terms of congruence conditions of $p$ and $n$) for which $x^{2}+1$ irreducible over $\mathbb{F}_{p^{n}}$.