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Can you give me some examples of infinitely generated modules over commutative rings, other than $A[x_1,\ldots,x_n,\ldots]$?

Thanks a lot!

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    @Michalis Please consider converting the three comments to an answer, so that this question gets removed from the [unanswered tab](http://meta.math.stackexchange.com/q/3138). If you do so, it is helpful to post it to [this chat room](http://chat.stackexchange.com/rooms/9141) to make people aware of it (and attract some upvotes). For further reading upon the issue of too many unanswered questions, see [here](http://meta.stackexchange.com/q/143113), [here](http://meta.math.stackexchange.com/q/1148) or [here](http://meta.math.stackexchange.com/a/9868).2013-06-16

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One variable is enough! $A[X]$ over $A$ is infinitely generated as an $A$-module.

Other suggestions in the comments: $\mathbb{Q}$ over $\mathbb{Z}$ or an infinite direct sum of copies of $\mathbb{Z}$ over $\mathbb{Z}$.

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    @Manny: thanks! That makes sense.2013-06-17