Exponentiation in power series fields

Details Exponentiation in power series fields Exponentiation in power series fields

1996-08-15

arxiv.org/abs/math/9608214v1

Proc. Amer. Math. Soc. 125 (1997), 3177--3183

Mathematics

Commutative Algebra

Scientific paper

We prove that for no nontrivial ordered abelian group G, the ordered power series field R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that there is a non-surjective logarithm. For an arbitrary ordered field k, no exponential on k((G)) is compatible, that is, induces an exponential on k through the residue map. This is proved by showing that certain functional equations for lexicographic powers of ordered sets are not solvable.

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