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

Published online by Cambridge University Press:  12 March 2014

Krzysztof Krupiński
Krzysztof Krupiński*
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław. Poland, E-mail: kkrup@math.uni.wroc.pl
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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.

Keywords

ω-categorical groupω-categorical ringsmall compact G-groupsmall compact G-ring03C4503C3520A15

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1403 - 1417
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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