Jacobson-Bourbaki Correspondence Theorem for Noncommutative Rings
Jacobson-Bourbaki Correspondence Theorem for Noncommutative Rings
复制标题
非交换环的雅各布森-布尔巴基对应定理
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Zhang Jiangang
中科院分区：
文献类型：
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作者：
Feng Jiangchao;Shen Ran;Zhang Jiangang
在代数中，雅各布森-布尔巴基定理对于有限、正规和可分域扩张的伽罗瓦理论的推广特别有用。这是由雅各布森领域和扩大到司环的雅各布森和嘉当谁归功于未发表的工作布尔巴基。2005年，Winter提出了交换环的Jacobson-Bourbaki对应定理。这个关于增广环的定理是Kadison在2012年提出的。本文证明了中心上生成的非交换环的Jacobson-Bourbaki定理。我们建立了A中右有限余维的剖分集与A的加法自同态End A在其中心上生成的Galois环集之间的双射对应。
In algebra，the Jacobson-Bourbaki theorem is especially useful for generalizations of the Galois theory of finite， normal and separable field extensions． It was obtained by Jacobson for fields and extended to division rings by Jacobson and Cartan who credited the result to unpublished work by Bourbaki． In 2005，the JacobsonBourbaki correspondence theorem for commutative rings was formulated by Winter． And this theorem for augmented rings was formulated by Kadison in 2012． In this paper，we prove the Jacobson-Bourbaki theorem for noncommutative rings which is finitely generated over their centers． We establish a bijective correspondence between the set of subdivisions which are right finite codimension in A and the set of Galois rings of the additive endomorphisms End A of A which is finitely generated over its center．