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All Journal Journal of Natural Sciences and Mathematics Research UNEJ e-Proceeding Jurnal Matematika Sains dan Teknologi Desimal: Jurnal Matematika Teorema: Teori dan Riset Matematika M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika PRISMATIKA: Jurnal Pendidikan dan Riset Matematika Vygotsky: Jurnal Pendidikan Matematika dan Matematika Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Joong-Ki
Suroto Suroto
Departement Of Mathematics, Universitas Jenderal Soedirman
Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Chemistry Education Environmental Science Materials Science & Nanotechnology Mathematics Physics Social Sciences Other

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

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Ideals In Matrix Rings Over Commutative Rings Mugi Lestari; Suroto Suroto; Niken Larasati
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 Achmad Abdurrazzaq Agung Prabowo agus sugandha Agustini Tripena Ari Wardayani Ari Wardayani, Ari Ari Wardayanti Chumaedi Sugihandardji Fajar Hoeruddin Fatkhur Rozi Guswanto, Bambang Hendriya Mashuri Mashuri Mugi Lestari Nadya Novika Najmah Istikaanah Najmah Istikaanah Niken Larasati Siti Rahmah Nurshiami, Siti Rahmah slamet riyadi Sri Maryani Sri Maryani