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Journal : M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika

Ideals In Matrix Rings Over Commutative Rings Lestari, Mugi; Suroto, Suroto; Larasati, Niken
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 8 No. 4 (2023): Mathline: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v8i4.481

Abstract

In this research, we discuss about ideal of matrix rings over commutative rings and its properties. The research of ideal in matrix rings is important because it is the basic structure for constructing factor rings in matrix rings. This research is a literature research that examines and develops research that has been done previously. We develop ideal concepts in an usually ring into matrix rings over commutative rings. By showing the sufficient and necessary condition of ideal of matrix rings over commutative rings, we show the form of ideal in matrix rings over commutative rings. Then, by using the properties of two ideal in a ring, we show the properties of intersection, addition and multiplication of two ideal in matrix rings over commutative rings. The result of this research is the form of ideal in matrix rings over commutative rings is the set of all matrices over the ideal in commutative rings. Then, the intersection, addition and multiplication of two ideal in matrix rings over commutative rings is also an ideal of matrix rings over commutative rings.
Co-Authors Abdul Hamid Adiarso, Adiarso Afrimansyah, Mohammad Haris Agung Pranoto Agus Sugiyono Amalia Nuril Hidayati Amalia, Rizqi Dwinanda Anggeraini , Via Gusti Apriliana, Silfia Marca Atika Ari Wardayani, Ari Arief Firmanto Arjo, Waldetrudis Kamona Arya Aditya Yudha Aslamiah Azizah, Fajriyati Nur Cantika, Putri Riau CHOIRUN NISA Disantara, Fradhana Putra dwi purwanto Eka Cahya Muliawati Eka Kartika Untari Erni Erni Estiwardani, Riswanda Fadliyana Ekawaty Febrianti, Fosa Natalia Feriandy, Dicky Ilham Firdaus, Ahmad Rizki Firnanda, Muhammad Yusron Fitriyanti, Ririn Aunia Furoidah, Ayu Hayati, Allatifah Nurul Hidayat, Nabiilah Salmaa Dhiyaa Husna, Nadia Idha Sihwaningrum Iftita Ziyan Amalia Izzatika, Amrina Latifah, Lailatul Leswara, Dianita Febrina Luri Mekeama Maya Amelia Putri Mubayyina, Al- Mugi Lestari, Mugi Munaisra Tri Tirtaningsih Mutia Nur Estri, Mutia Nur Nurhasanah, Hasna Nuri Alvita, Stefani Nurmalita, Anindia Octaviani, Peppy Oskar Skarayadi, Oskar Padmasari, Siwi Perdana, Dayu Rika Prayoga, Sigit Puspita Dewi, Ratna Etie Qusnul Khotimah, Nimas Rahmah, Syafira Atika Rara Wardhani Rina Reorita Riziq, Muhammad Miftah Rosita, Melia Eka Saadati, Rahma Alfi Sapitri, Indah Nur Shanti Pujilestari, Shanti Siti Nuraini Siti Rahmah Nurshiami, Siti Rahmah Sugiyono Sugiyono Sulistyoningrum, Tri Puji Sulyani, Agnesia Candra Supriyadi Supriyadi Suroto Suroto Syahyeri, Afrizal Triyani Triyani Triyani Triyani Ulfah, Halida Ulvia, Rengganis Usep Kustiawan Valentino, Widhi Wardhani, Rara Wijono, Agung Wildani, Sahril Windi Astuti Windi Zamrudy Wulandadari, Christina Asri Wulandari, Desvia Wulandari, Sephia yudiartono, yudiartono Yuni Andriani Yunike Juniarti Fitria Yusmansyah*, Erfizal Fikri Zaitin, Mukharomah Zuhair Aulia, Teuku Muhammad Zahid