Primfaktorzerlegung von 1 {\displaystyle 1} in Z [ i ] {\displaystyle \mathbb {Z} [i]} :
1 ∈ Z [ i ] × {\displaystyle 1\in \mathbb {Z} [i]^{\times }} und daher ist 1 {\displaystyle 1} per Definition nicht prim.
![{\displaystyle \mathbb {Z} [i]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ffa94e9e2e6d9e5e5373d5fafb954b902743fde)
![{\displaystyle 1\in \mathbb {Z} [i]^{\times }}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41cf5cb51a66c4baa84c2ef136e79b60df4dab21)