An approach between the multiplicative and additive structure of a Jordan ring

Abstract

Let $${{\mathfrak {J}}}\, $$ and $${{\mathfrak {J}}}\, ^{'}$$ be Jordan rings. In this paper we study the additivity of n-multiplicative isomorphisms from $${{\mathfrak {J}}}\, $$ onto $${{\mathfrak {J}}}\, ^{'}$$ and of n-multiplicative derivations of $${{\mathfrak {J}}}\, $$ . Suppose that $${{\mathfrak {J}}}\, $$ contains a nontrivial idempotent; we prove that if $${{\mathfrak {J}}}\, $$ satisfying certain conditions, then n-multiplicative maps and n-multiplicative derivations from $${{\mathfrak {J}}}\, $$ to $${{\mathfrak {J}}}\, ^{'}$$ are additive maps.

Topics & Concepts