Jacobson猜想成立的某些充分条件

Some Sufficient Conditions for Jacobson's Conjecture

中文关键词:  限制李代数  Jacobson猜想  p半线性映射  半单元素

英文关键词:restricted Lie algebras  Jacobson's conjecture  semisimple elements  p-semilin-ear mappings.

中文摘要:

      Jacobson在文献[1]给出了一个猜想:若(L,[p])为限制李代数,且x^[p]n(x)=x,?x∈L,n(x)>0,则L是交换李代数.至今为止,人们还不知此猜想是否正确.本文分别证明这个猜想在p映射为p半线性映射或者域F为代数闭域条件下的正确性.

英文摘要:

      Jacobson conjectured that every restricted Lie algebra (L,[p]) satisfying the requirement x^[p]n(x)= x and n(x) > 0 for every x ∈ L is abelian. So far, people haven't still known whether the conjecture is true. There are some sufficient conditions for Jacobson's conjecture in the paper.