When are multiplicative mappings additive?

Additivity of Jordan Triple Product Homomorphisms on Generalized Matrix Algebras

“…Characterizing the interrelation between the multiplicative and additive structures of a ring or algebra is an interesting topic. This question was first studied by Martindale [18] who showed the surprising result that every bijective multiplicative map from a prime ring containing a nontrivial idempotent onto an arbitrary ring is necessarily additive. For operator algebras, the same problem was treated in [1,14,21].…”

On Commutativity of Semiprime Rings with Multiplicative (Generalized)-derivations

“…Inspired by the work of Martindale III (Martindale, 1969), Daif (Daif, 1991) introduced the concept of multiplicative derivations. Accordingly, a map f : R → R is called multiplicative derivation of R if f (xy) = f (x)y + x f (y) holds for all x, y ∈ R. Of course, these maps are not necessarily additive.…”

Additivity of Jordan (Triple) Derivations on Rings

“…In recent years, there has been a great interest in the study of additivity of mappings on rings as well as operator algebras (see [3] - [8], and references therein). Most of these results focus on the additivity of multiplicative maps, Jordan (triple) multiplicative maps, and Jordan elementary maps on rings, triangular algebras, and operator algebras.…”

“…Theorem 1.1. ( [8]) Let R be a ring containing a family {e α : α ∈ Λ} of idempotents which satisfies…”