On the additivity of n-multiplicative isomorphisms, derivations, and related maps in axial algebras

Abstract

In this paper, we demonstrate that several classes of functions, specifically n-multiplicative isomorphisms, derivations, elementary maps, and Jordan elementary maps on a class of algebras that includes Jordan algebras with idempotents, J(a)-axial algebras and M(a,b)-axial algebras, are additive under appropriate conditions, which may be referred to as Martindale-type conditions. Furthermore, we answer the question left open in the recent article titled "Multiplicative isomorphisms and derivations on axial algebra."