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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 : Science and Technology Indonesia

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Commuting and Centralizing Maps on Modules Fitriani, Fitriani; Wijayanti, Indah Emilia; Faisol, Ahmad; Ali, Shakir
Science and Technology Indonesia Vol. 10 No. 3 (2025): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2025.10.3.690-697

Abstract

A ring is a mathematical structure composed of a set with two binary operations that follow certain axioms. One important function within a ring is the centralizing and commuting mapping, which has been extensively studied in recent decades. Commuting mappings are a special case of centralizing mappings. A module is a generalization of a ring. In this paper, we extend the concept of commuting mappings from ring to module structures. However, defining commuting mappings in modules presents a challenge, as multiplication is required for their definition, yet modules do not have this operation. Additionally, constructing nonzero centralizing and commuting mappings on modules is a nontrivial task. To address these challenges, we employ the concept of idealization as a framework for defining commuting mappings in modules. We also propose a method for constructing nonzero commuting mappings on modules by leveraging existing commuting mappings in rings. Specifically, if α is a commuting mapping on a ring T, then a corresponding commuting mapping α’ can be defined on the module by utilizing α. Moreover, we establish that the finite sum of commuting mappings is also a commuting mapping and that a linear combination of  commuting mappings is also a commuting mapping under certain conditions.
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