A Note on Finite Dimensional Subideals of Lie Algebras
نویسنده
چکیده
1.1 We prove that: Over any field I of characteristic p > 0, there exists an infinite dimensional Lie algebra which is the join of two (p + l)-dimensional and nilpotent (of class exactly p) subideals. A result of Hartley ([2; p. 259, theorems 2 and 5]) states that over any field of characteristic zero, the join of a pair of finite dimensional (resp. finite dimensional and nilpotent) subideals is finite dimensional (resp. finite dimensional and nilpotent) and a subideal. There is also an example ([2; p. 270]) in characteristic p > 0, of a join of two finite dimensional subideals which is not a subideal, but is finite dimensional. In our counter example the join is neither finite dimensional nor even a subideal.
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