Irreducible element

In abstract algebra, a non-zero non-unit element in an integral domain is said to be irreducible if it is not a product of two non-units.

Irreducible elements should not be confused with prime elements. (A non-zero non-unit element ${\displaystyle a}$ in a commutative ring ${\displaystyle R}$ is called prime if, whenever ${\displaystyle a|bc}$ for some ${\displaystyle b}$ and ${\displaystyle c}$ in ${\displaystyle R,}$ then ${\displaystyle a|b}$ or ${\displaystyle a|c.)}$ In an integral domain, every prime element is irreducible, but the converse is not true in general. The converse is true for unique factorization domains (or, more generally, GCD domains.)

...
Wikipedia