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

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...

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Veröffentlicht in:	The Journal of symbolic logic 2011-12, Vol.76 (4), p.1403-1417
1. Verfasser:	Krupiński, Krzysztof
Format:	Artikel
Sprache:	eng
Schlagworte:	03C35 03C45 20A15 Algebra Algebraic structure Coordinate systems Group structure Induction assumption Mathematical rings Model theory small compact G-group small compact G-ring Solvability Subrings Topological compactness ω-categorical group ω-categorical ring
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description	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.
doi_str_mv	10.2178/jsl/1318338856
format	Article
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subjects	03C35 03C45 20A15 Algebra Algebraic structure Coordinate systems Group structure Induction assumption Mathematical rings Model theory small compact G-group small compact G-ring Solvability Subrings Topological compactness ω-categorical group ω-categorical ring
title	On relationships between algebraic properties of groups and rings in some model-theoretic contexts
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