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Definability of Local Abelian Groups by Their Splitting Rings
Lobachevskii Journal of Mathematics Pub Date : 2020-11-07 , DOI: 10.1134/s1995080220090309 S. V. Vershina
中文翻译:
局部阿贝尔群通过裂环的可定义性
更新日期:2020-11-09
Lobachevskii Journal of Mathematics Pub Date : 2020-11-07 , DOI: 10.1134/s1995080220090309 S. V. Vershina
Abstract
This paper is devoted to the problem (Glaz, Vinsonhaler, Wickless): When a \(p\)-local torsion-free group is determined by the collection of its splitting rings? For \(p\)-local torsion-free groups with quadratic and cubic minimal splitting fields necessary and sufficient condition has been found according to which \(p\)-local group \(G\) is determined by the collection of its splitting rings.
中文翻译:
局部阿贝尔群通过裂环的可定义性
摘要
本文专门讨论这个问题(Glaz,Vinsonhaler,Wickless):当一个\(p \)-局部无扭群由其裂环的集合确定时?对于具有二次和三次最小分裂场的\(p \)-局部无扭组,找到了必要和充分条件,根据该条件,\(p \)-局部组\(G \)由其分裂集合确定戒指。