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

2025/02/17 by Daniel E. N. Kawai, Kawai, Daniel Eiti Nishida, Henrique Guzzo +3
Mathematics · #17C27 #17D99 #Advanced Topics in Algebra #FOS: Mathematics #Functional Equations Stability Results #Mathematical and Theoretical Analysis #Primary: 17A36 #Rings and Algebras (math.RA) #Secondary: 17A01

paper · pdf · doi:10.48550/arxiv.2503.21783

openalex publication_date 2025/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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."

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