ABSTRACT
An algebra J over a field F of characteristic 6= 2 is called Jordan if it satisfies the identities
xy = yx, (x2y)x = x2(yx). (1)
It is well known that a finite dimensional Jordan nil algebra is nilpotent [2], [6]. In particular, every solvable finite dimensional Jordan algebra is nilpotent. This result is not true any more for Jordan superalgebras: an example
of a finite dimensional solvable Jordan superalgebra that is not nilpotent is given in [4]. In fact, Jordan superalgebras behave more like Lie algebras; an odd part
of a Jordan superalgebra has a product “of Lie type.” But for Lie algebras, the ordinary notion of nilness is useless since every Lie algebra is nil of index 2. A proper substitution for this is the notion of an Engelian element: an element a of an algebra A is called Engelian if the operator of right multiplication Ra is nilpotent. The classical Engel Theorem states that a finite dimensional Lie algebra is nilpotent if and only if all its elements are Engelian [1]. This theorem admits also a generalization for finite dimensional Lie superalgebras [3].
