“…In [3], the authors proved that a map ϕ between two factor von Newmann algebras is a * -ring isomorphism if and only if ϕ({a, b} * ) = {ϕ(a), ϕ(b)} * . In [4], 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 used them to impose condition such that a map between C * -algebras is a * -ring isomorphism. Even more, in [16], Taghavi et al considered the product a • b = a * b + ba * and studied when a bijective map is additive in * -algebras.…”