A theorem on spherically complete valued abelian groups
环与代数
2008-02-03 v1
摘要
We give a criterion for a group homomorphism on a valued abelian group to be surjective and to preserve spherical completeness. We apply this to give a criterion for the existence of integration on a valued differential field. Further, we give a criterion for a sum of spherically complete subgroups of a valued abelian group to be spherically complete. This in turn can be used to determine elementary properties of power series fields in positive characteristic.
引用
@article{arxiv.math/9707233,
title = {A theorem on spherically complete valued abelian groups},
author = {Franz-Viktor Kuhlmann},
journal= {arXiv preprint arXiv:math/9707233},
year = {2008}
}