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There are polynomial rings in infinitely many indeterminates. Does it make sense to talk about power series rings in infinitely many indeterminates. If not, what do we get when we complete the polynomial ring $k[x_1,...]$ with respect to the maximal ideal $(x_1,...)$.

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You can certainly define a ring structure on power series in infinitely many variables, although I'm not sure if it would be the completion of $k[x_1,\ldots]$ wrt $(x_1,\ldots)$. –  Alex Becker Mar 9 '12 at 6:27
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That completion has only series with a finite number if terms of each degree. –  Mariano Suárez-Alvarez Mar 9 '12 at 6:35
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You get two different power series rings depending on whether the individual terms of a power series are allowed to contain infinitely many indeterminates. –  Ted Mar 9 '12 at 6:36

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