What are examples of irreducible but not prime elements?
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
127030
Simple example of non-arithmetic ring (non-distributive ideal lattice)
3037
Integral domain without unity has prime characteristic?
106914
Existence of Irreducible polynomials over $\mathbb{Z}$ of any given degree
10885
Existence of irreducible polynomials over finite field
133495
Example of a ring without Invariant Basis Property
135102
How do the definitions of "irreducible" and "prime" elements differ?
75558
Counter-example for prime ideals in a non commutative ring.
120673
Irreducible fibers of a closed subset implies irreducibility
160
homeomorphism non-example
84355
Methods to see if a polynomial is irreducible
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
28327
(Simple) Examples on Non-Commutative Rings
140550
Irreducible element iff prime norm in Gaussian integers?
140497
Irreducibles are prime in a UFD
34798
Example of element of double dual that is not an evaluation map
152109
In a UFD if $x$ is irreducible, then $(x)$ is prime