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

TL;DR

This paper investigates conditions under which n-multiplicative maps and derivations between Jordan rings are additive, focusing on the structure of Jordan rings with nontrivial idempotents.

Contribution

It establishes that under certain conditions, n-multiplicative maps and derivations in Jordan rings are additive, bridging multiplicative and additive structures.

Findings

n-multiplicative maps are additive under specific conditions

n-multiplicative derivations are additive with nontrivial idempotents

connects multiplicative structures with additive properties in Jordan rings

Abstract

Let J and J' be Jordan rings. We prove under some conditions that if J contains a nontrivial idempotent, then n-multiplicative maps and n-multiplicative derivations from J to J' are additive maps.