Year: 2026
Type: article
Abstract: Homoderivations represent a generalized differential operator that combines multiplicative and derivational properties, making them significant in studying algebraic structures with hybrid operations. This paper initiates the systematic study of homoderivations on prime near rings, an algebraic structure where only left distributivity holds. We establish the foundational Leibniz formula and investigate when the existence of such mapping forces the underlying near ring to become commutative. Specificall, we prove that if a 2-torsion free prime near ring admits a non zero homoderivation h with h([x,y])=0 or h(x◦y)=0, then N is a commutative ring. Furthermore, we characterize the center of the near ring through the behavior of homoderivations on square closed Lie ideals. These results have implications for understanding the interplay between ring theoritic derivation and multiplicative mappings in non ring.
DOI: 10.20956/zsw81k91
Authors: Gusti Ayu Dwi Yanti, Sandy Salomo Saruan
Institutions: Universitas Gadjah Mada, Bandung Institute of Technology
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7213468077