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All Journal MATEMATIKA CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society 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 Pepadun 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.
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.
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.
Hybrid Hill Cipher ASCII 256 and RSA Cipher in Securing Messages Sandi Saputra; Fitriani Fitriani; Ahmad Faisol; Wamiliana Wamiliana; Siti Laelatul Chasanah
Jurnal Pepadun Vol. 6 No. 3 (2025): December
Publisher : Department of Computer Science, Faculty of Mathematics and Natural Sciences, University of Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.23960/pepadun.v6i3.284

Abstract

Secure communication requires encryption methods that strike a balance between efficiency and key protection. This study proposes a hybrid cryptosystem integrating the Hill Cipher and the RSA Cipher. The Hill Cipher, based on modular matrix multiplication, achieves fast encryption but lacks secure key distribution, whereas RSA provides robust asymmetric key management at a higher computational cost. By encrypting the Hill Cipher key with RSA, the proposed method strengthens resistance to brute-force and key compromise attacks. A Python-based implementation was developed and tested on messages of varying lengths. Experimental results show that the hybrid system maintains the efficiency of the Hill Cipher while significantly improving key security, with time complexity increasing modestly due to RSA key operations. Two scenarios were analyzed depending on whether the message length is divisible by the key matrix size, confirming the scheme’s flexibility. This approach demonstrates a practical and secure solution for protecting digital communication against cryptanalysis.
(α, β)-Derivation on Matrix Ring Mn(R) Dania Azzahra; Fitriani Fitriani; Ahmad Faisol
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.
The Connection Between Jordan Derivations and Nilpotent Derivations on 2-Torsion-Free Semiprime Rings Rahmah Mutiara Ayu Ningtiyas; Fitriani Fitriani; Ahmad Faisol
Jambura Journal of Mathematics Vol 8, No 2: August 2026
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v8i2.37723

Abstract

Let R be a ring. A derivation on a ring is an additive map that satisfies the Leibniz rule d(ab) = d(a)b + ad(b), for every a, b ∈ R. A derivation d on a ring R is called a nilpotent derivation if there exists a natural number n such that dⁿ(R) = 0. This research studies nilpotent Jordan derivations on 2-torsion-free semiprime rings. Motivated by the results of Brešar, Chung, and Luh on Jordan derivations and nilpotent derivations, the study aims to analyze their nilpotency patterns and the behavior of inner derivations generated by nilpotent elements. Using a deductive literature-study approach through mathematical proofs and examples, we show that if d²ⁿ(R) = 0 for some n ∈ N, then d²ⁿ⁻¹(R) = 0. Consequently, every nonzero nilpotent Jordan derivation has an odd nilpotency index. In addition, for a nilpotent element P ∈ R with nilpotency index n, the inner derivation dₚ(x) = [p, x] is nilpotent with nilpotency index at most 2n − 1. These results contribute to a deeper understanding of derivation structures on 2-torsion-free semiprime rings.
Co-Authors . Wamiliana Aang Nuryaman Adelia, Lisa Ahmad Faisol Ahmad Rizki Wiranto Akmal Junaidi Ambarwati, Yuli Ananto Adi Nugraha Andriani, Jessica Attiya Yuliana Azis, Dorrah Budi Surodjo Dania Azzahra 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 Muslim Ansori 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 Rahmah Mutiara Ayu Ningtiyas Rahmawati, Rara Gusti Rinanda, Selvi Diana Dwi Rudi Ruswandi Rudi Ruswandi Sandi Saputra Setyaningsih, Nevi SHAKIR ALI Siti Khabibah Siti Laelatul Chasanah Siti Laelatul Chasanah Siti Laelatul Chasanah, Siti Laelatul Sitompul, Desi Elena Tresya Carmela Purba Trisnawati, Evi Utami, Bernadhita Herindri Samodera Waluyo, Ridho Wamiliana ., Wamiliana Wamiliana Wamiliana Wesly Agustinus Pardede Widiarti Widiarti Yesi Santika Yudi Antoni Yunita Septriana Anwar