On relationships between algebraic properties of groups and rings in some model-theoretic contexts

2010/07/04 by Krzysztof Krupiński, Krzysztof Krupinski, Krupinski, Krzysztof · 1 citation
Mathematics · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.LO #msc:03C35 #msc:03C45 #msc:20A15

paper · pdf · doi:10.48550/arxiv.1007.0532

arxiv created 2010/07/04 · arxiv updated 2010/07/06

Abstract

We study relationships between certain algebraic properties of groups and rings definable in a first order structure or *-closed in a compact G-space. As a consequence, we obtain a few structural results about ω-categorical rings as well as about small, nm-stable compact G-rings, and we also obtain surprising relationships between some conjectures concerning small profinite groups.

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• On ω-categorical groups and rings with NIP

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