The Properties of the Rn Module over the Matrix Ring Mn×n(R)
- 10.2991/apr.k.220503.014How to use a DOI?
- Module; Torsion module; Prime module; Multiplication module; Faithdul module
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).
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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 -