Dimensional groups and fields

2015/11/30 by Frank Olaf Wagner, Wagner, Frank Olaf · 1 citation
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1511.09272

openalex publication_date 2015/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Superrosy dependent groups having finitely satisfiable generics

Cited by

• On the cohomology of finite-dimensional nilpotent groups and Lie rings

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