Jordan derivations on triangular matrix rings

TL;DR

This paper investigates conditions under which a specific type of map on triangular matrix rings becomes additive, extending previous research on the additivity of algebraic maps.

Contribution

It establishes new conditions on triangular matrix rings that ensure a map satisfying a specific symmetry condition is additive.

Findings

Identifies conditions for additivity of maps on triangular matrix rings

Extends previous work on algebraic map additivity

Provides a framework for analyzing similar maps in ring theory

Abstract

Guided by the research line introduced by Martindale III in [1] on the study of the additivity of maps, this article aims establish condi- tions on triangular matrix rings in order that an map ' satisfying '(ab + ba) = '(a)b + a'(b) + '(b)a + b'(a) for all a; b in a triangular matrix ring becomes additive.