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Preprint Number 598

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598. Jan Dobrowolski and Krzysztof Krupiński
Locally finite profinite rings
E-mail: ,

Submission date: 25 June 2013.

Abstract:

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 G-rings, where we also obtain a description of possible actions of G on the underlying ring.

Mathematics Subject Classification: 16W80, 16N20, 16N40, 20E18, 20F50, 03C45, 03E15

Keywords and phrases: locally finite profinite ring, small compact G-ring, small profinite ring

Full text arXiv 1306.5970: pdf, ps.


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