Es sei P ∈ Z [ X ] {\displaystyle {}P\in \mathbb {Z} [X]} ein ganzzahliges normiertes Polynom, dass in Q [ X ] {\displaystyle {}\mathbb {Q} [X]} irreduzibel sei. Zeige, dass P {\displaystyle {}P} auch in Z [ X ] {\displaystyle {}\mathbb {Z} [X]} irreduzibel ist.
![{\displaystyle {}P\in \mathbb {Z} [X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/96640dda8654067fada15427cd44953ee42398be)
![{\displaystyle {}\mathbb {Q} [X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05854fb7f5090d865105d7297fa178c8eb802fbf)
![{\displaystyle {}\mathbb {Z} [X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/192c251bd578fa7224f44f5d4539c9813b31aa46)