Proceedings of the Soedirman International Conference on Mathematics and Applied Sciences (SICOMAS 2021)

The Properties of the Rn Module over the Matrix Ring Mn×n(R)

Authors
Triyani Triyani1, *, Ari Wardayani1, Alfalfa Amruhasanah1
1Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Jenderal Soedirman, Jl. dr. Suparno, 61, Grendeng, Purwokerto Utara, 53122, Jawa Tengah, Indonesia.
*Corresponding author. Email: triyani@unsoed.ac.id
Corresponding Author
Triyani Triyani
Available Online 25 May 2022.
DOI
https://doi.org/10.2991/apr.k.220503.014How to use a DOI?
Keywords
Module; Torsion module; Prime module; Multiplication module; Faithdul module
Abstract

This paper discusses the properties of the Rn module over the matrix ring Mn×n(R) related to the torsion module, prime module, multiplication module, and faithful module. The study results concluded that the Rn module over the matrix ring Mn×n(R) is a torsion module because each element of Rn is a torsion element. The Rn module is also a prime module because the zero element of Rn is a prime submodule. Moreover, the Rn module over the matrix ring Mn×n(R) is also a multiplication module because there exists an ideal presentation I = Mn×n(U) where U is ideal of ring R. However, the Rn module is not a faithful module because the annihilator of Rn does not contain only zero element of matrix ring Mn×n(R).

Copyright
© 2022 The Authors. Published by Atlantis Press International B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license.

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Volume Title
Proceedings of the Soedirman International Conference on Mathematics and Applied Sciences (SICOMAS 2021)
Series
Advances in Physics Research
Publication Date
25 May 2022
ISBN
978-94-6239-579-4
ISSN
2352-541X
DOI
https://doi.org/10.2991/apr.k.220503.014How to use a DOI?
Copyright
© 2022 The Authors. Published by Atlantis Press International B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license.

Cite this article

TY  - CONF
AU  - Triyani Triyani
AU  - Ari Wardayani
AU  - Alfalfa Amruhasanah
PY  - 2022
DA  - 2022/05/25
TI  - The Properties of the Rⁿ Module over the Matrix Ring Mn×n(R)
BT  - Proceedings of the Soedirman International Conference on Mathematics and Applied Sciences (SICOMAS 2021)
PB  - Atlantis Press
SP  - 65
EP  - 68
SN  - 2352-541X
UR  - https://doi.org/10.2991/apr.k.220503.014
DO  - https://doi.org/10.2991/apr.k.220503.014
ID  - Triyani2022
ER  -