what is Z[x] in the sense of a unique factorization domain

Question

The wikipedia page on unique factorization domains gives the following example.

What does the notation Z[something] mean?

Answer 1

Given a ring extension $S\supseteq R$ and an element $\alpha\in S$ one denotes by $$ R[\alpha] $$ the smallest subring of $S$ containg $R$ and $\alpha$.

In the above example, $R=\Bbb Z$ and $\alpha=\zeta_n$, a primitive $n$-th root of unity.

The ring $\Bbb Z[\zeta_n]$ is the ring of integers in the cyclotomic field $\Bbb Q(\zeta_n)$.

References form this site:

Adjoining an element to a ring

Adjoining to a ring