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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Ahmad Faisol
Department of Mathematics, Faculty of Science and Mathematics, Universitas Lampung, Indonesia
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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ALGEBRAIC PROPERTIES OF JORDAN TRIPLE DERIVATIONS ON RING R Rachma Allya Shieffa; Fitriani Fitriani; Ahmad Faisol; Wamiliana Wamiliana; Thomas Juliansyah
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp3025-3034

Abstract

Polynomial rings play a fundamental role in algebra, with wide-ranging applications in number theory, algebraic geometry, and analysis. A key method for studying ring structures is through derivations. Among these, Jordan triple derivations generalize Jordan derivations and exhibit more intricate structural properties. While Jordan derivations have been extensively studied, their triple counterparts remain relatively underdeveloped, particularly in the context of polynomial rings. This paper adopts a theoretical algebraic approach to investigate the properties and structural aspects of Jordan triple derivations on rings and the polynomial ring R[x]. By extending existing results and constructing illustrative examples, we establish several new properties. In particular, we show that the set of Jordan triple derivations is closed under finite addition, finite linear combinations, and finite direct sums. Furthermore, every inner derivation is shown to be a Jordan triple derivation. Moreover, any Jordan triple derivation on the ring induces a Jordan triple derivation on the polynomial ring . These results contribute to a deeper understanding of the structure of Jordan triple derivations and provide a foundation for further research in this area.
Co-Authors Fitriani Fitriani Rachma Allya Shieffa Thomas Juliansyah Wamiliana Wamiliana