If $a$ is a zero of $f(x)$ in some extension of $F$, show that $g(x)$ is irreducible over $F(a)$, given $f(x)$ and $g(x)$ are
127310
Suppose $\gcd(\deg(f),\deg (g))=1$. Show that $g(x)$ is irreducible in $k(\alpha)[X]$.
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
35959
irreducibility of a polynomial over $\mathbb{F}_2$
80547
If $0$ is the zero-object $ \Longrightarrow F(0) $ is the zero object when $F$ additive
142093
The closure of an irreducible subset of an irreducible space is irreducible.
89514
Show that if $g \circ f$ is injective, then so is $f$.
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
10885
Existence of irreducible polynomials over finite field
25439
f(a) = inverse of a is an isomorphism iff a group G is Abelian
90144
Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
4296
If $f,g$ are entire functions and$\ fg\equiv 0$ then either $f \equiv 0$ or $g\equiv0. $
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
1487
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
121714
Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
145573
How to show that $f$ is a zero function?
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$