Additivity of Maps on Triangular Algebras

TL;DR

This paper proves that certain bijective maps on triangular algebras, including multiplicative and Jordan maps, are inherently additive, revealing a fundamental algebraic property.

Contribution

It establishes the additivity of various bijective maps on triangular algebras, a property not previously confirmed for these classes of maps.

Findings

Multiplicative bijective maps are additive.

Jordan bijective maps are additive.

Jordan triple bijective maps are additive.

Abstract

We prove that every multiplicative bijective map, Jordan bijective map, and Jordan triple bijective map from a triangular algebra onto any ring is automatically additive.