A study of $3$-derivations and their algebraic implications
نویسندگان
1 Department of Mathematics, Azarbaijan Shahid Madani University, P.O. Box 53751, Tabriz, Iran.
2 Department of Mathematics, Azarbaijan Shahid Madani University, P.O. Box 53751, Tabriz, Iran.
doi
10.30504/jims.2025.520461.1257چکیده
This paper explores the concept of $3$-derivations, in the context of algebras. Building on prior work that established the invariance of primitive ideals, prime ideals, and minimal prime ideals under derivations, we extend these results to the case of $3$-derivations. In particular, we show that several properties of primitive and prime ideals, previously proven for derivations, also hold in the setting of $3$-derivations. Furthermore, we examine $3$-derivations on triangular Banach algebras and show that a linear map $\mathcal{D}:\mathcal{T}\rightarrow\mathcal{T}$ qualifies as a $3$-derivation if satisfies certain structural conditions.
