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Unverified Commit 2aa5070e authored by rrueger's avatar rrueger
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Algebra I: Modules. Add remark regarding analogy between cyclic modules and cyclic groups

parent 5394912b
......@@ -80,7 +80,8 @@
\begin{definition}
Let $M$ be an $R$-module. Then $M$ is said to be a \textbf{cyclic module} if
$M = Rx = \{ ax \mid a \in R\}$ where $x \in M$.
$M = Rx = \{ ax \mid a \in R\}$ where $x \in M$. This is in direct analogy to
a cyclic group, namely they are both generated by one element.
\end{definition}
Clearly, $R$ itself is a cyclic $R$-module as we have $R = R1$. If $M = Rx$ then
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