On The Derivations And An Extension Of Malcev Algebras

After introducing some preliminaries and notations, the dissertation investigates semisimple Malcev algebras, giving some equivalent definitions and properties of semisimple Malcev algebras.And then, an extension of Malcev algebras, M = M+R(N) (vector space direct sum), is discussed, where the linear space R(N) is spanned by Rn(right multiplication) for all n N(M),N(M) being the J- nucleus of a Malcev algebra M. It is shown that M is solvable (nilpotent, semisimple) if and only if M is.