How do we localise a the ring of formal power series $\mathbb C[[x, y]]$ to get the field of multivariate Laurent series $\mathbb C((x))((y))$? If $S_x$ and $S_y$ are the multiplicative closed sets $\{x^n: n\geq0\}$ and $\{y^n: n\geq0\}$, respectively, do we have $$S_y^{-1}S_x^{-1}\mathbb C[[x, y]]=\mathbb C((x))((y))?$$
2026-03-29 06:55:22.1774767322
Ring of formal multivariate Laurent series as a consecutive localisation
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