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cbarker1

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Dear Everyone,

I am stuck with an exercise problem. The problem states from Dummit and Foote Ed. 2

My attempt:

Example: When $n=6=3\cdot 2$, then the only element will be $\overline{3*2}$ in $\Bbb{Z}/6\Bbb{Z}$.

Proof: Suppose $n=a^{k}b$ for some $a,b \in \Bbb{Z}$. (Do I need some cases? If so, three cases?)

Thanks,

Cbarker1

I am stuck with an exercise problem. The problem states from Dummit and Foote Ed. 2

*Abstract Algebra*: "An element $x$ in $R$ (where $R$ is a ring with 1) is called nilpotent if $x^{m}=0$ for some $m \in \Bbb{Z}^{+}$. Show that if $n=a^{k}b$ for some $a,b \in \Bbb{Z}$, then $\overline{ab}$ is a element of $\Bbb{Z}/n\Bbb{Z}$."My attempt:

Example: When $n=6=3\cdot 2$, then the only element will be $\overline{3*2}$ in $\Bbb{Z}/6\Bbb{Z}$.

Proof: Suppose $n=a^{k}b$ for some $a,b \in \Bbb{Z}$. (Do I need some cases? If so, three cases?)

Thanks,

Cbarker1

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