Lie Isomorphisms in Prime Rings with Involution
Lie Isomorphisms in Prime Rings with Involution
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DOI：
10.1006/jabr.1994.1286
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发表时间：
1994-10
影响因子：
0.9
通讯作者：
K. Beidar;W. S. Martindale;A. Mikhalev
中科院分区：
文献类型：
--
作者：
K. Beidar;W. S. Martindale;A. Mikhalev
摘要设R和R ‘是具有第一类对合的素环，它们分别具有斜元K和K ’的李子。进一步设(RC: C)≠1,4,9,16,25,64，其中C为R的扩展质心。证明了K到K ‘上的任何李同构可以唯一地推广到一个< K >到< K ’ >上的结合子同构，其中< K >和< K ‘ >分别是K和K ’生成的结合子。
Abstract Let R and R ′ be prime rings with involutions of the first kind and with respective Lie subrings of skew elements K and K ′. Furthermore assume ( RC : C ) ≠ 1, 4, 9, 16, 25, 64, where C is the extended centroid of R . It is shown that any Lie isomorphism of K onto K ′ can be extended uniquely to an associative isomorphism of 〈 K 〉 onto 〈 K ′〉, where 〈 K 〉 and 〈 K ′〉 are respectively the associative subrings generated by K and K ′.