On The Nilpotence Of Lie Triple Algebras

In the first part of this paper, we mainly concerned about the nilpotence of Lie triple algebras. We gave the definition of nilpotence at first and obtained results as follows: If Lie triple algebra is nilpotent, then its standard enveloping Lie algebra is nilpotent. In the second part of the paper, we defined an extension of Malcev algebra and obtained that Malcev algebra is nilpotent (solvable) if and only if its extension is nilpotent(solvable).