A theorem on spherically complete valued abelian groups

1997/07/30 by Franz-Viktor Kuhlmann, Franz‐Viktor Kuhlmann, Kuhlmann, Franz-Viktor
Mathematics · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Mathematical and Theoretical Analysis #math.RA

paper · pdf · doi:10.48550/arxiv.math/9707233

arxiv created 1997/07/30 · arxiv updated 2009/11/30

Abstract

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.

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