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.
"On relationships between algebraic properties of groups and rings in some model-theoretic contexts." J. Symbolic Logic 76 (4) 1403 - 1417, December 2011. https://doi.org/10.2178/jsl/1318338856