Kommutativer Ring/Restklassenring/Idealpotenzen/Aufgabe

Sei

{}R

ein kommutativer Ring mit zwei Idealen

{}{\mathfrak {a}},{\mathfrak {b}}\subseteq R

. Es sei

{}S=R/{\mathfrak {b}}

und

{}{\tilde {\mathfrak {a}}}={\mathfrak {a}}S

das Bildideal. Zeige, dass

{}{\mathfrak {a}}^{n}S={\tilde {\mathfrak {a}}}^{n}

ist.

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