Exponentiation in power series fields

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dc.creatorKuhlmann, Franz-Viktor
dc.creatorKuhlmann, Salma
dc.creatorShelah, Saharon
dc.date1996-08-15
dc.date.accessioned2026-07-07T09:15:36Z
dc.date.available2026-07-07T09:15:36Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/math/9608214
dc.identifierhttp://arxiv.org/abs/math/9608214
dc.identifierProc. Amer. Math. Soc. 125 (1997), 3177--3183
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153073
dc.subjectCommutative Algebra
dc.subjectLogic
dc.subjectRings and Algebras
dc.titleExponentiation in power series fields
dc.typetext

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