CX/Restklassenring/Isomorphietyp/Aufgabe

Zeige, dass jeder echte Restklassenring von ${}\mathbb {C} [X]$ isomorph zu einem Produktring der Form

\mathbb {C} \times \cdots \times \mathbb {C} \times \mathbb {C} [X]/(X^{2})\times \cdots \times \mathbb {C} [X]/(X^{2})\times \mathbb {C} [X]/(X^{3})\times \cdots \times \mathbb {C} [X]/(X^{3})\times \cdots \times \mathbb {C} [X]/(X^{m})\times \cdots \times \mathbb {C} [X]/(X^{m})

ist.

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