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Is it true that $\mathbb{C}\otimes_\mathbb{Z}\mathbb{C}=\mathbb{C}$?

This is not the homework. I just want to know what it is and I cannot find it any text I have.

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    What do you mean with "what is..."? Do you know what $\mathbb{C}$, $\mathbb{Z}$ and the tensor product '$\otimes$' are? Be a bit more specific!2012-10-24
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    @Sh4pe I think the user wants a nice description of this group.2012-10-24
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    Right, I changed the question.2012-10-24
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    The two are definitely not equal in a set-theoretic sense, but then this is hardly ever the case (the non-negative integers are not _equal_ to $\Bbb N$ either, strictly speaking). So you are asking about some kind of isomorphism; as the answers show it depends on what kind of isomorphism (sets, abelian groups, $\Bbb C$-vector spaces) you are interested in.2012-10-24

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