# The Construction of Armendariz Ring using Formal Triangle Matrix Ring

## Authors

• Aidah Nabilah Anwar Student
• Amir Kamal Amir
• Nurdin Hinding

## Keywords:

Trinion, Quaternion, BImodule, Ring, Formal Triangle Matrix Ring, Armendariz Ring

## Abstract

Trinion and Quaternion numbers are one of the hypercomplex numbers which is an extensions of the complex number. From Trinion and Quaternion numbers, a bimodule can be formed which is an ordered pair of Trinion and Quaternion. Furthermore, Trinion number, Quaternion number, and their bimodule can be formed into a  Formal Triangle Matrix. The Formal Triangle Matrix is better known as the Upper Triangle Matrix. Since Trinion number, Quaternion number and their bimodule are rings, then the Formal Triangle Matrix can be called as the Formal Triangular Matrix Ring. The purpose of this study is to construct the Armendariz Ring using the Formal Triangular Matrix Ring. The obtained results will show that the Formal Triangular Matrix Rings are the -Skew Armendariz Ring and the -Skew -Armendariz Ring, where  is a Ring Endomorphism and  is -derivation.

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2023-01-05

## How to Cite

Anwar, A. N., Amir, A. K., & Hinding, N. (2023). The Construction of Armendariz Ring using Formal Triangle Matrix Ring. Jurnal Matematika, Statistika Dan Komputasi, 19(2), 304-316. https://doi.org/10.20956/j.v19i2.23263

## Section

Research Articles

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