Lie Derivations on Skew Elements in Prime Rings With Involution
Lie Derivations on Skew Elements in Prime Rings With Involution
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DOI：
10.4153/cmb-1987-049-5
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发表时间：
1987-09
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影响因子：
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通讯作者：
Eleanor Killam
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文献类型：
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作者：
Eleanor Killam
设R是满足x/2∊R的素环，当x∊R时，设R有两个和不为1的非平凡对称幂等元e1，e2，且由e1，e2，1-(e1+e2)决定的子环在其中心上不是不超过4维的单环的阶.然后，如果L是K到R的斜元的Lie导子，则存在R的子环A，A⊆，导子D：A→RC，R的中心闭包，以及映射T：R→C，满足K上的L=D+T且=0.
Abstract Let R be a prime ring with involution satisfying x/2 ∊ R whenever x ∊ R. Assume that R has two nontrivial symmetric idempotents e1, e2 whose sum is not 1, and that the subrings determined by e1, e2, 1 — (e1 + e2) are not orders in simple rings of dimension at most 4 over their centers. Then if L is a Lie derivation of the skew elements K into R there exists a subring A of R, A ⊆ , a derivation D :A → RC, the central closure of R, and a mapping T:R → C, satisfying L = D + T on K and = 0.