The Construction of Armendariz Ring using Formal Triangle Matrix Ring

Authors

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

DOI:

https://doi.org/10.20956/j.v19i2.23263

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.

References

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Published

2023-01-05

Issue

Section

Research Articles

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