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All Journal MATEMATIKA Wahana Matematika dan Sains 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 Limits: Journal of Mathematics and Its Applications 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
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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Journal : Integra: Journal of Integrated Mathematics and Computer Science

 1 
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.
Co-Authors . Wamiliana Aang Nuryaman Adelia, Lisa Ahmad Rizki Wiranto Akmal Junaidi Ananto Adi Nugraha Andriani, Jessica Citra Puspa Tria 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 Lucia Ratnasari Muammar, Muhammad Fikri Muslim Ansori Nabilla Yolanda Paramitha Nevi Setyaningsih Nikken Prima Puspita Notiragayu Notiragayu Notiragayu Nurhamidah Nurhamidah Nurlela Nurlela Nusyirwan Nusyirwan Octavia, Megawati Pardede, Wesly Agustinus Rahma, Aira Rahmawati, Rara Gusti Rizki Agung Wibowo Rudi Ruswandi Rudi Ruswandi Saidi, Subian Sam Wibowo Setyaningsih, Nevi SHAKIR ALI Silvi Fitriani Siti Khabibah Siti Laelatul Chasanah Siti Laelatul Chasanah, Siti Laelatul Siti Rugayah Sitompul, Desi Elena Stacia Litha Suryani Suryani, Stacia Litha Trisnawati, Evi Waluyo, Ridho Wesly Agustinus Pardede Wibowo, Sam Yunita Septriana Anwar