11 research outputs found
Locally finite profinite rings
We investigate the structure of locally finite profinite rings. We classify
(Jacobson-) semisimple locally finite profinite rings as products of complete
matrix rings of bounded cardinality over finite fields, and we prove that the
Jacobson radical of any locally finite profinite ring is nil of finite
nilexponent. Our results apply to the context of small compact -rings, where
we also obtain a description of possible actions of on the underlying ring.Comment: 17 page
Model theory of Galois actions of torsion Abelian groups
We show that the theory of Galois actions of a torsion Abelian group is
companionable if and only if for each prime , the -primary part of is
either finite or it coincides with the Pr\"{u}fer -group. We also provide a
model-theoretic description of the model companions we obtain