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If only one of the variables needs to be invertible, one could work with Laurent series in one variable over a power series ring in the other variable; or conversely, power series in one variable over a Laurent series ring in the other variable:

sage: L.<z> = LaurentSeriesRing(QQ)
sage: P.<u> = PowerSeriesRing(L)

or

sage: P.<u> = PowerSeriesRing(QQ)
sage: L.<z> = LaurentSeriesRing(P)

In some cases it might be enough to use a polynomial ring or a Laurent polynomial ring for one of the variables.