Hahn Series

In mathematics, Hahn series (sometimes also known as Hahn-Mal'cev-Neumann series) are a type of formal infinite series. They are a generalization of Puiseux series (themselves a generalization of formal power series) and were first introduced by Hans Hahn in 1907 (and then further generalized by Anatoly Maltsev and Bernhard Neumann to a non-commutative setting). They allow for arbitrary exponents of the indeterminate so long as the set supporting them forms a well-ordered subset of the value group (typically or ). Hahn series were first introduced, as groups, in the course of the proof of the Hahn embedding theorem and then studied by him as fields in his approach to Hilbert's seventeenth problem.