Dedekindbereich/Gebrochenes Ideal/Idealdarstellung/Aufgabe

Zeige, dass man jedes gebrochene Ideal ${}{\mathfrak {f}}$ in einem Dedekindbereich ${}R$ in der Form

{}{\mathfrak {f}}={\mathfrak {a}}\cdot {\mathfrak {b}}^{-1}\,

mit Idealen ${}{\mathfrak {a}}$ und ${}{\mathfrak {b}}$

darstellen kann.

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