$\overline{Y}$ is irreducible in $A:=\Bbb{C}[X,Y]/ (X^2-Y^3)$.
87101
Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
44502
An irreducible polynomial cannot share a root with a polynomial without dividing it
17670
If $p\in R[X_1,\dots,X_n]$ is irreducible, is it still irreducible in $R[X_1,\dots,X_n,\dots,X_N]$?
41693
Use irreducible fibers to show $X$ is irreducible
18717
Proof for Irreducible Error statement in ISLR page 19
97729
Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
84355
Methods to see if a polynomial is irreducible
77620
Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
143095
If an $H\le G$ has an irreducible representation of dimension $d$, then show $G$ has an irreducible representation of at least dimension $d$.
32391
Show that $x^2+x+4$ is irreducible over $\mathbb Z_{11}$.
31215
Irreducible cyclotomic polynomial
142093
The closure of an irreducible subset of an irreducible space is irreducible.
70537
Irreducible polynomials have distinct roots?
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
141792
Slick proof the determinant is an irreducible polynomial
91356
Irreducibility of an infinite sequence of polynomials