How to show that $x$ is irreducible in $\frac{\mathbb R[x,y]}{(x^2+y^2-1)}$?
65435
Ring of trigonometric functions with real coefficients
156671
Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime
134726
Show the polynomial is irreducible in $\textbf Z_2$
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
96087
Let $\mathbb{F}_2 \cong \mathbb{Z}/2\mathbb{Z}$. Is $x^4+x^2+1$ irreducible in $\mathbb{F}_2[x]$?
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
70537
Irreducible polynomials have distinct roots?
20790
What are irreducibles in the ring $R$ of entire functions?
65558
Irreducible in $\mathbb{Z}[\sqrt{-5}]$
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
100573
Show that $x^4-10x^2+1$ is irreducible over $\mathbb{Q}$
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
2043
$X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
87101
Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$