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
- 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.
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 - 10.2991/apr.k.220503.014 ID - Triyani2022 ER -