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I'm reading this paper and am wondering if the quote below found on page 17 near the bottom makes sense.

We need a way to produce a $B\otimes C-A\otimes C$ bimodule: to do this consider the module $M\otimes_k C$.

What is a $B\otimes C-A\otimes C$ bimodule? Or is this a typo?

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    Do you know what a bimodule is? – 2017-02-23
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    @QiaochuYuan I know what a bimodule is but I've never seen that notation before. How do I read that? Is it just $B\otimes C$ minus $A\otimes C$? – 2017-02-23
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    A bimodule is a left module over one ring and a right module over another ring. That notation names the two rings. – 2017-02-23
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    @QiaochuYuan That clears it up, so you could also write $_{B\otimes C}M_{A\otimes C} $. – 2017-02-23
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    Yes, exactly. $\,$ – 2017-02-28

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