Triangle Is Deduced On Algebra - Lie Can Guide Map

In this paper, using method of algebra decomposition, we mainly discuss ε-Lie derivable maps by Jordan zero products, partial ε-Lie derivable maps on triangular algebras and nontrivial nest algebras. The details as following:In chapter1. some notions, definitions (for example, triangular algebra, ε-Lie derivable maps and so on) and a well-known theorem are given.In chapter2. we mainly discuss ε-Lie derivable maps on triangular algebras by Jordan zero products and get the form of linear map δ satisfying δ([A,B]ε)=[δ(A). B]ε+[4.δ(B)]ε with A o B=0on triangular algebras. We also discuss ε-Lie derivable maps on nontrivial nest algebras by Jordan zero products.In chapter3. we get a characterization of partial ε-Lie derivable maps on trian-gular algebras. As an application, it is proved that a linear map on nontrivial nest algebras is a partial ε-Lie derivable map if and only if it is an inner derivation.