It is well known that the ring of formal power series over a field $K[[x_1,x_2,\ldots,x_n]]$ is an UFD. My question is the following: the ring $K[[x_1,\ldots,x_n]][x_1^{-1},\ldots,x_n^{-1}]$ is also UFD? I was not able to find any reference on such a result.
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2Yes, it is a UFD because the localization of a UFD is also a UFD. – Jesko Hüttenhain Aug 05 '18 at 11:21
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But it is a localization?! With respect to which multiplicatively closed set? Maybe the set of monomials in $K[x_1,\ldots,x_n]$? – Mircea Aug 05 '18 at 15:45
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The set of monomials will work perfectly, or you can think of it as a sequence of $n$ localizations with respect to each of the variables. – Jesko Hüttenhain Aug 05 '18 at 18:03
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Thank you for your answer. – Mircea Aug 06 '18 at 09:10