# Localization of power series and module structure

Let $R=\mathbb{Q}[X,Y]$ be the polynomial ring of two commuting variable. Let $S$ be the multiplicative subset of $R$ generated by homogeneous linear polynomials. Let also $\widehat{R}$ be the ring of formal power series in $X,Y,$ and $\widehat{R}_S$ be the localization of $\widehat{R}$ at $S.$ $\widehat{R}_S$ is a $R-$module in the natural way. Let $\widehat{R}_S^0$ be the quotient $\widehat{R}_S/\mathbb{Q},$ all three considered as Abelian groups.

Question: Is there a $R-$module structure on $\widehat{R}_S^{0},$ which makes the quotient map a morphism of $R-$modules?

The question showed up when trying to make a distribution valued modular symbol. The distributions map to power series via a Fourier transform. One kills the constants as one way to make the Manin relations work.

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