# The absolutely no part of tensor items of rated mods

I assure there is a very easy reference on this, but also for some factor I can not locate it. If you can aim me to a reference or simply write a brief evidence for me, I would certainly be really satisfied.

Offered a rated ring $R_{\bullet}$ and also a localization $R_{\bullet}^{*}$. We additionally have actually a rated $R_{\bullet}$-mod, $M_{\bullet}$.

So what I need to know; is $\left(R_{\bullet}^{*}\otimes M_{\bullet}\right)_0=\left(R_{\bullet}^{*}\right)_0\otimes \left(M_{\bullet}\right)_0$?

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2019-05-04 16:21:47
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For a counterexample, take $R=k[t]$ with its common grading and also $M=R(1)$, the free component of ranking one created in level $1$.