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All Journal MATEMATIKA Wahana Matematika dan Sains 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 Limits: Journal of Mathematics and Its Applications Jurnal Komputasi
Ahmad Faisol
Jurusan Matematika FMIPA, 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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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.
Homomorphisms of Modules over Two Skew Generalized Power Series Rings Ahmad Faisol; Fitriani Fitriani; Muslim Ansori; Budi Surodjo
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.1921

Abstract

Let R and R' be rings with identity and let S be a strictly ordered monoid equipped with twisting homomorphisms into the endomorphism rings of R and R'. Using these data, we consider two skew generalized power series rings associated with R and R'. Starting from an (R,R')-module M, we construct an induced module consisting of generalized power series with coefficients in M and show that it naturally becomes a module over the two skew generalized power series rings through a suitable trilinear action. We then study homomorphisms in this framework. In particular, we prove that every (R,R')-module homomorphism between two modules induces a corresponding homomorphism between their associated generalized power series modules. Furthermore, we provide sufficient conditions describing when a generalized power series belongs to the kernel of the induced homomorphism in terms of the coefficientwise behavior of the original map. These results extend the theory of skew generalized power series modules from the classical single-ring setting to a two-ring context and provide a foundation for further developments, including generalized isomorphism results and related algebraic applications.
Jordan Derivations on Semigroup Rings Pratama, Aprial Wayudi; Faisol, Ahmad; Fitriani, Fitriani
Jurnal Matematika Integratif Vol 22, No 2: Oktober 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n2.70088.1-14

Abstract

Let $R$ be a ring. An additive mapping $d : R \rightarrow R$ is called a Jordan derivation if it satisfies the identity $d(a^2) = d(a)a + ad(a)$ for every $a \in R$. In this paper, Jordan derivations are studied on the semigroup ring $R[S]$ in order to investigate their structural properties. The study begins with the construction of Jordan derivations on the semigroup ring $R[S]$, followed by an analysis of their algebraic properties and the relationship between Jordan derivations on $R$ and those on $R[S]$. Furthermore, several illustrative examples are presented to support the theoretical results obtained. The concept of Jordan derivations extends the understanding of algebraic structures through their application to semigroup rings.
Co-Authors . Wamiliana Aang Nuryaman Adelia, Lisa Ahmad Rizki Wiranto Akmal Junaidi Ananto Adi Nugraha Andriani, Jessica Ayuni, Fitri Budi Surodjo Citra Puspa Tria Dania Azzahra David Aji Saputra Dian Kurniasari Dian Kurniasari Dina Eka Nurvazly Dwiyanti, Gusti Ayu Eri Setiawan Eri Setiawan Fathudin Fathudin Fitri Ayuni Fitriani Fitriani Fitriani Hafifullah, Desfan Indah Emilia Wijayanti Jessica Andriani Khoirin Nisa Listiana Listiana Listiana Lucia Ratnasari Muammar, Muhammad Fikri Muslim Ansori Muslim Ansori Nabilla Yolanda Paramitha Nevi Setyaningsih Nikken Prima Puspita Notiragayu Notiragayu Notiragayu Nurhamidah Nurhamidah Nurlela Nurlela Nusyirwan Nusyirwan Octavia, Megawati Pardede, Wesly Agustinus Pratama, Aprial Wayudi Rahmah Mutiara Ayu Ningtiyas Rahmawati, Rara Gusti Rinanda, Selvi Diana Dwi Rizki Agung Wibowo Rudi Ruswandi Rudi Ruswandi Saidi, Subian Sam Wibowo Sandi Saputra Setyaningsih, Nevi SHAKIR ALI Silvi Fitriani Siti Khabibah Siti Laelatul Chasanah Siti Laelatul Chasanah Siti Laelatul Chasanah, Siti Laelatul Siti Rugayah Sitompul, Desi Elena Stacia Litha Suryani Suryani, Stacia Litha Trisnawati, Evi Utami, Bernadhita Herindri Samodera Waluyo, Ridho Wamiliana Wamiliana Wesly Agustinus Pardede Wibowo, Sam Yunita Septriana Anwar