Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

A study of $3$-derivations and their algebraic implications

Document Type : Research Article

Authors
S. Nazarlou
M. H. Sattari
Department of‎ Mathematics‎, Azarbaijan ‎Shahid Madani University‎, ‎P.O. Box 53751, Tabriz‎, ‎Iran.
10.30504/jims.2025.520461.1257
Abstract
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.
Keywords
Primitive ideal
prime ideal
triangular Banach algebra
Subjects
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Journal of the Iranian Mathematical Society
Volume 6, Issue 2
August 2025
Pages 159-172