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All Journal MATEMATIKA CAUCHY: Jurnal Matematika Murni dan Aplikasi Al-Jabar : Jurnal Pendidikan Matematika Science and Technology Indonesia Jurnal Matematika: MANTIK Desimal: Jurnal Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan J Statistika: Jurnal Ilmiah Teori dan Aplikasi Statistika Jambura Journal of Mathematics Jurnal Matematika UNAND Jurnal Pengabdian Kepada Masyarakat (JPKM) Tabikpun Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Jurnal Siger Matematika Journal of Fundamental Mathematics and Applications (JFMA) Jurnal Matematika Integratif Integra: Journal of Integrated Mathematics and Computer Science Jurnal Komputasi
Fitriani
Universitas Lampung
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Environmental Science Health Professions Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Social Sciences Transportation

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A STUDY OF DERIVATIONS AND LINEAR MAPPINGS ON SKEW GENERALIZED POWER SERIES MODULES Faisol, Ahmad; Fitriani, Fitriani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp3047-3058

Abstract

This paper investigates the structure of skew generalized power series modules over skew generalized power series rings, emphasizing the extension of derivations in this context. We define and study additive mappings that generalize classical derivations with respect to module homomorphisms and ring derivations. Under suitable compatibility conditions, we construct corresponding derivations on skew generalized power series modules and establish their fundamental properties. These findings contribute to a broader understanding of how derivations can be systematically extended from classical module theory to generalized algebraic frameworks.
On the Construction of Rough Quotient Modules in Finite Approximation Spaces Adelia, Lisa; Fitriani; Faisol, Ahmad; Anwar, Yunita Septriana
Integra: Journal of Integrated Mathematics and Computer Science Vol. 2 No. 1 (2025): March
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20252116

Abstract

Let S be a set and φ an equivalence relation on S. The pair (S, φ) forms an approximation space, where the relation φ partitions S into mutually disjoint equivalence classes. For any subset B' ⊆ S, the lower approximation Apr(B') is defined as the union of all equivalence classes entirely contained in B', while the upper approximation Apr(B') is the union of all equivalence classes that have a non-empty intersection with B'. The subset B' is called a rough set in (S, φ) if Apr(B') ≠ Apr(B'). If, in addition, B' satisfies certain algebraic conditions, it is termed a rough module. This paper investigates the construction of rough quotient rings and rough quotient modules within such approximation spaces. The approach is developed using finite sets to facilitate the algebraic formulation and analysis of these rough structures.
Algebraic Construction of Rough Semimodules Over Rough Rings Trisnawati, Evi; Fitriani; Faisol, Ahmad; Anwar, Yunita Septriana
Integra: Journal of Integrated Mathematics and Computer Science Vol. 1 No. 2 (2024): July
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20241219

Abstract

Let (℧, µ) be an approximation space, where ℧ is a non-empty set and µ is an equivalence relation on ℧. For any subset H ⊆ ℧, we can define the lower approximation and the upper approximation of H . A set H is called a rough set if its lower and upper approximations are not equal. In this study, we explore the algebraic structure that emerges when certain binary operations are defined on rough sets. Specifically, we investigate the conditions under which a subset H forms a rough semimodule over a rough semiring. We present several key erties of this structure and construct illustrative examples to support our theoretical results.
Jordan Derivation on the Polynomial Ring R[x] Sitompul, Desi Elena; Fitriani; Chasanah, Siti Laelatul; Faisol, Ahmad
Integra: Journal of Integrated Mathematics and Computer Science Vol. 2 No. 2 (2025): July
Publisher : Magister Program of Mathematics, Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/integrajimcs.20252229

Abstract

Given a ring R. An additive mapping δ: R → R is called a Jordan derivation if δ(a²) = δ(a)a + aδ(a) for every a in R. Jordan derivation is one of the special forms of derivation. In this study, we investigate the Jordan derivation on the polynomial ring R[x] and examine its properties. This study begins by constructing the Jordan derivation on the polynomial ring R[x], followed by investigating its characteristics, including the relationship between the Jordan derivation on the ring R and on the polynomial ring R[x]. In addition, several concrete examples are presented to illustrate the main results obtained. This research is expected to contribute to a deeper understanding of the properties of Jordan derivations on polynomial rings.
Pelatihan LaTeX Menggunakan Overleaf untuk Meningkatkan Kemampuan Penulisan Karya Ilmiah bagi Dosen di Pringsewu Fitriani, Fitriani; Faisol, Ahmad; Nuryaman, Aang; Kurniasari, Dian; Utami, Bernadhita Herindri Samodera
Jurnal Pengabdian Kepada Masyarakat (JPKM) TABIKPUN Vol. 5 No. 3 (2024)
Publisher : Faculty of Mathematics and Natural Sciences - Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23960/jpkmt.v5i3.184

Abstract

Keunggulan LaTeX telah menjadikannya sebagai standar dalam penulisan karya ilmiah. Saat ini, sebagian dosen belum dapat menggunakan LaTeX sehingga diperlukan pelatihan penggunaan Latex bagi Dosen di Pringsewu Lampung. Kegiatan ini bertujuan untuk meningkatkan kemampuan penulisan karya ilmiah bagi para Dosen. Kegiatan ini dilaksanakan di Institut Bakti Nusantara (IBN) Pringsewu dengan metode ceramah interaktif dan praktik langsung menggunakan Overleaf. Keuntungan menggunakan overleaf adalah peserta tidak perlu mengunduh aplikasi untuk menjalankan LaTeX. Pada sesi terakhir, beberapa peserta mempresentasikan hasil kerjanya. Selanjutnya, peserta diberikan kuesioner mengenai tingkat pemahaman peserta terhadap materi yang diberikan. Kegiatan ini diikuti oleh 34 dosen di Pringsewu. Berdasarkan hasil kuisioner, sebanyak 76,47% peserta memahami materi dengan sangat baik, 20,59% memahami dengan baik dan 2,94% cukup memahami materi yang diberikan. Selain itu, sebanyak 97,06% peserta tertarik menulis artikel menggunakan LaTeX.
NIL DERIVATIONS AND d-IDEALS ON POLYNOMIAL RINGS Mursyidah, Ditha Lathifatul; Fitriani, Fitriani; Utami, Bernadhita Herindri Samodera; Faisol, Ahmad
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0325-0334

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.
Penentuan Invers Matriks Tridiagonal Dengan Algoritma Lewis David Aji Saputra; Ahmad Faisol; Fitriani
Jurnal Komputasi Vol. 13 No. 2 (2025)
Publisher : Jurusan Ilmu Komputer Fakultas MIPA Universitas Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23960/komputasi.v13i2.312

Abstract

Matriks tridiagonal merupakan jenis matriks bujursangkar yang hanya memiliki elemen tidak nol pada diagonal utama, superdiagonal, dan subdiagonal. Matriks jenis ini sering muncul dalam penyelesaian sistem persamaan linear serta dalam berbagai penerapan komputasi numerik. Salah satu tantangan utama dalam penggunaan matriks tridiagonal adalah menentukan inversnya secara efisien. Penelitian ini bertujuan untuk menentukan invers matriks tridiagonal menggunakan Algoritma Lewis, yaitu metode berbasis rekursif yang memanfaatkan pola hubungan antar elemen untuk menghasilkan invers dengan lebih cepat dan efisien, khususnya untuk matriks berdimensi besar dan sparse. Penelitian ini dilakukan secara analitik dan diperkuat dengan implementasi menggunakan bahasa pemrograman Python. Hasil penelitian menunjukkan bahwa Algoritma Lewis mampu menentukan invers matriks tridiagonal secara sistematis dengan validasi melalui perkalian kembali matriks awal dan hasil invers yang menghasilkan matriks identitas.
(α, β)-Derivation on Matrix Ring Mn(R) Azzahra, Dania; Fitriani, Fitriani; Faisol, Ahmad
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 14 Issue 1 April 2026
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v14i1.37789

Abstract

In ring theory, a derivation is an additive mapping d:R→R satisfying Leibniz’s rule. A well-known generalization of this notion is the (α,β)-derivation, defined with respect to two ring endomorphisms α and β. In this paper, we study (α,β)-derivations on the matrix ring Mₙ(R) and several of its subrings, including scalar matrices, diagonal matrices, and upper and lower triangular matrix rings. It is shown that an (α,β)-derivation on the base ring RRR induces an (α′,β′)-derivation on these matrix subrings via entrywise extension, preserving their structural properties. Furthermore, we examine certain properties of (α,β)-derivations on the direct product ring R×R. In particular, we show that the sum of two (α,β)-derivations does not necessarily form an (α,β)-derivation, which is demonstrated through a counterexample.
Bi-derivation on Polynomial Ring Rinanda, Selvi Diana Dwi; Fitriani, Fitriani; Faisol, Ahmad
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.70123.1-18

Abstract

Derivations and their generalizations play an important role in understanding the structure of rings. One natural extension of derivations is the notion of a biderivation, which is a bi-additive mapping satisfying derivation-type identities in each argument. In this paper, we investigate biderivations on polynomial rings. Several examples of biderivations are constructed and some of their fundamental properties are established. In particular, we study the relationship between biderivations defined on a ring $R$ and those induced on the polynomial ring $R[x]$. The obtained results provide additional insight into the behavior of biderivations under polynomial ring extensions.
Co-Authors . Wamiliana Aang Nuryaman Adelia, Lisa Ahmad Faisol Ahmad Faisol Ahmad Rizki Wiranto Akmal Junaidi Ambarwati, Yuli Ananto Adi Nugraha Andriani, Jessica Attiya Yuliana Azis, Dorrah Azzahra, Dania David Aji Saputra Desiana Putri Dian Kurniasari Dian Kurniasari Dorrah Azis Dwiyanti, Gusti Ayu Fitri Ayuni Hafifullah, Desfan Indah Emilia Wijayanti Jessica Andriani Larasati Larasati Larasati Larasati Listiana Listiana Lucia Ratnasari M.G. Arma Yoga Pratama Mohamad Ibnu Hambali, Mohamad Ibnu Muammar, Muhammad Fikri Mursyidah, Ditha Lathifatul Muslim Ansori Muslim Ansori Mustofa Usman Nevi Setyaningsih Nikken Prima Puspita Notiragayu Notiragayu Notiragayu Notiragayu, Notiragayu Nurlela Nurlela Pardede, Wesly Agustinus Purba, Tresya Carmela Rahma, Aira Rahmawati, Rara Gusti Rinanda, Selvi Diana Dwi Rudi Ruswandi Rudi Ruswandi Setyaningsih, Nevi SHAKIR ALI Siti Khabibah Siti Laelatul Chasanah Siti Laelatul Chasanah, Siti Laelatul Sitompul, Desi Elena Tresya Carmela Purba Trisnawati, Evi Utami, Bernadhita Herindri Samodera Waluyo, Ridho Wamiliana ., Wamiliana Wesly Agustinus Pardede Widiarti Widiarti Yesi Santika Yudi Antoni Yunita Septriana Anwar