Jordan Derivations on Semigroup Rings

Pratama, Aprial Wayudi
Faisol, Ahmad
Fitriani, Fitriani

Jurnal Matematika Integratif
Vol 22, No 2: Oktober 2026

Let $R$ be a ring. An additive mapping $d : R \rightarrow R$ is called a Jordan derivation if it satisfies the identity $d(a^2) = d(a)a + ad(a)$ for every $a \in R$. In this paper, Jordan derivations are studied on the semigroup ring $R[S]$ in order to investigate their structural properties. The study begins with the construction of Jordan derivations on the semigroup ring $R[S]$, followed by an analysis of their algebraic properties and the relationship between Jordan derivations on $R$ and those on $R[S]$. Furthermore, several illustrative examples are presented to support the theoretical results obtained. The concept of Jordan derivations extends the understanding of algebraic structures through their application to semigroup rings.