Hahn series

Summary

A Hahn series is a formal sum $\sum_\gamma a_\gamma t^\gamma$ with coefficients in a field and exponents in a linearly ordered group. Its set of exponents must be well-ordered. Hahn series generalise formal power series and formal Laurent series to exponents that may be fractions, reals, or elements of any ordered abelian group. They form a field with a natural valuation, and these fields are a main source of examples of valued and ordered fields.