Locally finite profinite rings

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• 作者：Jan Dobrowolski ; Krzysztof Krupi艅ski
• 关键词：16W80 ; 16N20 ; 16N40 ; 20E18 ; 20F50 ; 03C45 ; 03E15
• 刊名：Journal of Algebra
• 出版年：1 March, 2014
• 年：2014
• 卷：401
• 期：Complete
• 页码：161-178
• 全文大小：302 K

文摘

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.