Near Perfect Ideals Of N-Lie Algebras

First the concepts of near perfect ideals and maximal near perfect ideals NP(L)of n-Lie algebras L over an algebraically closed field F of characteristic zero are introduced.The relationship between NP(L)and the lower center series,the structure of quotient algebras L/NP(L),and near perfect products are discussed.The main conclusions are:1)NP(L)is the minimum term of the lower center series;2)L/NP(L)is nilpotent;3)for nonzero near perfect ideal exists a set of regular near perfect product.Second the structure of n-Lie algebras with dim NP(L)=1,2 is studied.The main conclusions are:1)if dim NP(L)?2,then NP(L)is an abelian ideal;2)if dim NP(L)=2,and L1 is abelian ideal,then dim L1?dim L-n+1.At last of the paper,the structure of(n+3)-dimensional n-Lie algebras with dim NP(L)=0,1,2 is discussed,and classification is given.It is proved that there are 8 classes of(n+3)-dimensional n-Lie algebras L with dim NP(L)=0,5 classes of L with dim NP(L)=1,and 13 classes of L with dim NP(L)=2,and concrete multiplication of them is provided.