A Hahn series over a field with exponents in an ordered abelian group is a formal sum whose nonzero exponents form a well-ordered set. Such series form the Hahn series field.
For an ordered abelian group , the Hahn series field consists of formal sums with well-ordered support in . The least exponent defines a valuation with value group .
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A Hahn series is a formal power series that arises in the context of ordered groups and valuation theory. Specifically, it is used to describe a way to represent elements of certain fields, particularly in relation to ordered abelian groups.