Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Articles

NIL DERIVATIONS AND d-IDEALS ON POLYNOMIAL RINGS

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  • Ditha Lathifatul Mursyidah,
  • Fitriani Fitriani,
  • Bernadhita Herindri Samodera Utami,
  • Ahmad Faisol
Ditha Lathifatul Mursyidah
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, Indonesia
Fitriani Fitriani
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, Indonesia
Bernadhita Herindri Samodera Utami
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, Indonesia
Ahmad Faisol
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, Indonesia
DOI: https://doi.org/10.30598/barekengvol20iss1pp0325-0334
Published November 24, 2025
Keywords
  • d-ideal,
  • Linear combinations,
  • Nil derivation,
  • Polynomial ring
How to Cite
[1]
D. L. Mursyidah, F. Fitriani, B. H. S. Utami, and A. Faisol, “NIL DERIVATIONS AND d-IDEALS ON POLYNOMIAL RINGS”, BAREKENG: J. Math. & App., vol. 20, no. 1, pp. 0325-0334, Nov. 2025.

Copyright (c) 2025 Ditha Lathifatul Mursyidah, Fitriani Fitriani, Bernadhita Herindri Samodera Utami, Ahmad Faisol

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

Let  be a ring. An additive mapping  is called derivation if  satisfies Leibniz's rule, i.e.,   for every   In a special case, for each  there exists a positive integer  which depends on  such that , then  is called as a nil derivation on . The concept of - ideal which is an ideal that remains stable under the derivation operation . This research presents a systematic construction of nil derivations on polynomial rings and investigates their corresponding nilpotency indices. Unlike prior studies that often treat derivations in abstract terms, this work emphasizes explicit constructions, offering concrete examples and techniques for generating such derivations. A key focus is the relationship between nil derivations and general nilpotent derivations, including an analysis of their linear combinations. Furthermore, the study provides new insights into the behavior of nil derivations in the context of d-ideals, shedding light on their structural properties within ring theory. To enhance understanding, each theoretical development is supported by illustrative examples, reinforcing the applicability and significance of the results.

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