Exponentiation in power series fields
交换代数
2008-02-03 v1 逻辑
环与代数
摘要
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.
引用
@article{arxiv.math/9608214,
title = {Exponentiation in power series fields},
author = {Franz-Viktor Kuhlmann and Salma Kuhlmann and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9608214},
year = {2008}
}