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I don't think these series are Laurent series for two reasons: the powers do not need to be bounded below, and they do not need to be integers. What do the sources say? Deltahedron ( talk) 12:44, 8 February 2014 (UTC) reply

You're correct. The source simply defines a ring by saying the elements are of the form described in the article and define the multiplication explicitly. This is not the best way since we want to, for example, ${\displaystyle \mathbf {Z} [\Gamma ]}$ to be a subring of the Novikov ring. cf. [1] -- Taku ( talk) 13:05, 8 February 2014 (UTC) reply