Dimensional groups and fields

Frank Olaf Wagner

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arXiv · 1511.09272

Dimensional groups and fields

Frank Olaf Wagner

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Abstract

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that pseudofinite groups contain big finite-by-abelian subgroups, and pseudofinite groups of dimension 2 contain big soluble subgroups.

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Frank Olaf Wagner. 2015-11-30. Dimensional groups and fields. https://arxiv.org/abs/1511.09272

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