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I'm reading these lecture notes here about the tensor product and the author uses $M^\vee$ where $M$ is an $R$-module. Look at page 2 for an example (example 2.1). What does it mean? I looked through the notes but I couldn't find the definition. Many thanks for your help!

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I do not see where this notation is used on page 8. – Qiaochu Yuan Apr 3 '11 at 9:27
@Qiaochu: sorry, that was a typo, it should've said page 3! – Matt N. Apr 3 '11 at 9:30
It should've said page 2, not page 3. The file has been updated. – KCd Oct 13 '11 at 15:04

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$M^{\vee}$ (which in $\LaTeX$ is not a \wedge) is the dual $R$-module; that is, it's the $R$-module of all $R$-module homomorphisms $M \to R$, or more concisely it's $\text{Hom}_R(M, R)$. This is why the author refers to the dual pairing on page 2.

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Thank you so much! I didn't know what to search for because I didn't know it was called 'dual'. – Matt N. Apr 3 '11 at 9:33

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