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All Journal MATEMATIKA 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 Jurnal Siger Matematika Journal of Fundamental Mathematics and Applications (JFMA) Jurnal Matematika Integratif
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Journal : Journal of Fundamental Mathematics and Applications (JFMA)

 1 
IDEMPOTENT MATRIX OVER SKEW GENERALIZED POWER SERIES RINGS Ahmad Faisol; Fitriani Fitriani
Journal of Fundamental Mathematics and Applications (JFMA) Vol 5, No 1 (2022)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1002.148 KB) | DOI: 10.14710/jfma.v5i1.11644

Abstract

Let $R[[S,\leq,\omega]]$ be a skew generalized power series ring, with $R$ is a ring with an identity element, $(S,\leq)$ a strictly ordered monoid, and $\omega:S\rightarrow End(R)$ a monoid homomorphism. We define  the set of all matrices over $R[[S,\leq,\omega]]$, denoted by $M_{n}(R[[S,\leq,\omega]])$. With the addition and multiplication matrix operations, $M_{n}(R[[S,\leq,\omega]])$ becomes a ring. In this paper, we determine the sufficient conditions for $R$, $(S,\leq)$, and $\omega$, so the element of $M_{n}(R[[S,\leq,\omega]])$ is an idempotent matrix. 
ROUGH RINGS, ROUGH SUBRINGS, AND ROUGH IDEALS Fakhry Asad Agusfrianto; Fitriani Fitriani; Yudi Mahatma
Journal of Fundamental Mathematics and Applications (JFMA) Vol 5, No 2 (2022)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v5i2.15194

Abstract

The basic concept in algebra that is set theory can be expanded into rough sets. Basic operations on the set such as intersections, unions, differences, and complements can still apply to rough sets. In addition, one of the applications of rough sets is the use of rough matrices in decision making. Furthermore, mathematical or informatics researchers who work on rough sets connect the concept of rough sets with algebraic structures (groups, rings, and modules) so that a concept called rough algebraic structures is obtained. Since the research related to rough sets is mostly carried out at the same time, different concepts have emerged related to rough sets and rough algebraic structures. In this paper, other definitions of rough ring and rough subring will be given along with related examples and theorems. Furthermore, it will also be defined the left ideal and the right ideal of the rough ring along with examples. Finally, we will discuss the theorem regarding rough ideals.
Co-Authors . Wamiliana Abdiel Bellamy Thomas Ahmad Faisol Ahmad Rizki Wiranto Akmal Junaidi Ambarwati, Yuli Ananto Adi Nugraha Attiya Yuliana Desfan Hafifullah Desiana Putri Dian Kurniasari Dorrah Azis Fakhry Asad Agusfrianto Fitri Ayuni Gusti Ayu Dwiyanti Jessica Andriani Larasati Larasati Listiana Listiana Lucia Ratnasari M.G. Arma Yoga Pratama Megawati Octavia Mohamad Ibnu Hambali, Mohamad Ibnu Muslim Ansori Muslim Ansori Mustofa Usman Nevi Setyaningsih Nikken Prima Puspita Nikken Prima Puspita Notiragayu Notiragayu Notiragayu Nurlela Nurlela Rudi Ruswandi Siti Khabibah Siti Laelatul Chasanah Siti Rugayah Tresya Carmela Purba Wamiliana ., Wamiliana Wesly Agustinus Pardede Widiarti Widiarti Yesi Santika Yudi Antoni Yudi Mahatma