Catchup 7
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@@ -82,10 +82,10 @@ $$
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**Definition**. Given a commutative ring $R$ with identity, and $r \in R$, the set
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$$
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<a> = (r)R = \{ ar : r \in R \}
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\langle a \rangle = (r)R = \{ ar : r \in R \}
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$$
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is an ideal in $R$. Specifically, $<a>$ is a *principal ideal*.
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is an ideal in $R$. Specifically, $\langle a \rangle$ is a *principal ideal*.
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**Example**. Theorem 16.25. Every ideal in $\mathbb{Z}$ is a principal ideal.
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