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All Journal Jurnal Pengajaran MIPA Jurnal Sains Dasar Jurnal Sains dan Teknologi Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam Journal of the Indonesian Mathematical Society Dharmakarya : Jurnal Aplikasi Ipteks Untuk Masyarakat Journal of Mathematical and Fundamental Sciences Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA) Jurnal KARISMATIKA Indonesian Journal on Computing (Indo-JC) BAREKENG: Jurnal Ilmu Matematika dan Terapan JURNAL SILOGISME : Kajian Ilmu Matematika dan Pembelajarannya FIBONACCI: Jurnal Pendidikan Matematika dan Matematika Edsence: Jurnal Pendidikan Multimedia Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Jurnal Ilmiah Matematika Journal of Software Engineering, Information and Communication Technology JES-MAT (Jurnal Edukasi dan Sains Matematika) Jurnal Matematika Integratif Mathematical Sciences and Applications Journal Integrated : Journal Of Information Technology and Vocational Education Indonesian Journal of Applied Mathematics and Statistics Diophantine Journal of Mathematics and Its Applications Jurnal Pemanfaatan Teknologi untuk Masyarakat
Sisilia Sylviani
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Universitas Padjadjaran
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A Conceptual Summary of the Application of Free Modules in the Applied Mathematical Science Khairiah Rahmah Virda Sari; Sisilia Sylviani
Indonesian Journal of Applied Mathematics and Statistics Vol. 3 No. 1 (2026): Indonesian Journal of Applied Mathematics and Statistics (IdJAMS)
Publisher : PT Anugrah Teknologi Kecerdasan Buatan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.71385/idjams.v3i1.24

Abstract

Modules are one of the topics studied in algebra, furthermore there are free modules which are a subtopic of the module itself. This literature aims to find out the application of free modules in various branches of mathematics, both explicitly described and implicitly discussed in previous literatures. So that, this research used the Systematic Literature review to find the applications of module theory, especially the application of free modules in previous research. There are applications of free modules in various fields that are quite often discussed in system control theory, representation theory, cryptography, and mathematical physics. This research reveals that free modules not only play a role in pure algebra theory, but also have practical applications in various other sectors of science. This research is useful for future research to find out the application of modules, especially free modules, to research them in more depth.
Foundations of Krein Spaces and the Nonequivalence of Pythagorean Orthogonality Bagas Reynalda; Sisilia Sylviani; Anita Triska
Indonesian Journal of Applied Mathematics and Statistics Vol. 3 No. 1 (2026): Indonesian Journal of Applied Mathematics and Statistics (IdJAMS)
Publisher : PT Anugrah Teknologi Kecerdasan Buatan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.71385/idjams.v3i1.35

Abstract

This paper presents a fundamental analysis of the Krein Space, which is an indefinite generalization of the Hilbert Space. The Krein Space (K, [·,·]) is equipped with an indefinite inner product [·,·], which satisfies all the properties of a standard inner product except for positive definiteness. The absence of the positive definite property allows for the classification of elements based on their indefinite inner product with themselves into positive, negative, and neutral elements. The Krein space is formally defined through a canonical decomposition K = K+ [Å] K-, where K+ and K- are indefinitely orthogonal subspaces, both of which become Hilbert Spaces after adjusting the sign of their indefinite inner product. This decomposition induces a Canonical Symmetry Operator J, which allows the indefinite inner product to be related to a definite inner product <·,·> through the relation <x,y> = [J x, x].  This relationship defines the induced Hilbert Space norm ll · ll on K, where ll x ll2 = [J x, x]. The main focus of this paper is to demonstrate that indefinite orthogonality in Krein Space fundamentally differs from Hilbert Space orthogonality, particularly concerning the Nonequivalence of the Pythagorean orthogonality.
Co-Authors Achiaa, Amma Aisyah, Ranti Rivani Al Affiani, Hanifah Alamsyah, Alifa Raida Albari, Fardan Barkah Albertus Kusuma Seta Prawatya Alifiandi Nursanni Wiriadikusumah Alit Kartiwa Anita Triska Asep Singgih Aurillya Queency Ayung Candra Padmasari Ayung Candra Padmasari Bagas Reynalda Betty Subartini Bonyah, Ebenezer Cahyadi, Arya Raditya Candra Permana, Fahmi Dian Rinjani Dian Rinjani Edi Kurniadi Edi Kurniadi Edi Kurniadi Elah Dewia Ema Carnia Fahmi Candra Permana Fahmi Candra Permana Faldiyan, Muhammad Faza, Novan Ramadhani Nur Firdaus, Hamidah 'Alina Firmansyah, Feri Hidayatullah Fitriani agustina Gyenin, Mary Hadi, A.N. Hanni Garminia Hardiva, Ramadhina Hermawan, Aldi intan permata sari Intan Permata Sari Isah . Aisah Isah Aisah Kadir, M.P Karunia Eka Lestari Khairiah Rahmah Virda Sari Laily Wadil Muqadas Laksana, Andzar Tsaqif Maharani, Saskia Putri Maraya, N.S. Maya Purnama Sari Maya Purnama Sari Meishrin, Ishlahrahmi Mokhammad Ridwan Yudhanegara Muhammad Arief Budiman Muhammad Deni Johansyah Muhammad Zaky Zachary Muhammad Zaky Zachary Nugraha, Edwin Setiawan Nurendra Ari Wiguna Nursanti Anggriani Oktaviani, D. Pernanda Putra, Hazel Pratiwi, P.N Pudji Astuti Putri Nisa Pratiwi Putri, Estu Razanah, Khalilah Rio Guntur Utomo Risnawita Risnawita, Risnawita Setiawan, Ade Ripki Silvia Wijaya Suharto, Istiqomah Sukono Sukono Syamsiar, Syamsiar Tegar Ridwansyah Tielung, M. Fariel Fahriza Vimelia, Willen Wilopo, R. Yasmin, A. Zahra, N. Zaki Maulana Hidayat