Exponentiation in power series fields

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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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Commutative Algebra, Logic, Rings and Algebras

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http://salesiana.dossiersoluciones.com/handle/123456789/153073

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9608214
 http://arxiv.org/abs/math/9608214
 Proc. Amer. Math. Soc. 125 (1997), 3177--3183

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arXiv