“…In [4], the authors proved that a map Φ between two factor von Newmann algebras is a * -ring isomorphism if and only if Φ([X, Y ] * ) = [Φ(X), Φ(Y )] * . In [7], Ferreira and Costa extended these new products and defined two other types of applications, named multiplicative * -Lie n-map and multiplicative * -Jordan n-map and proved that, under certain conditions, an application between C * -algebras that is multiplicative * -Lie n-map and multiplicative * -Jordan n-map is a * -ring isomorphism. In the second paper of this series [6], Ferreira and Costa prove when a multiplicative * -Jordan n-map is a * -ring isomorphism.…”