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The Construction of Armendariz Ring using Formal Triangle Matrix Ring

Konstruksi Gelanggang Armendariz menggunakan Gelanggang Matriks Segitiga Formal

Jurnal Matematika, Statistika dan Komputasi · Vol. 19 No. 2 (2023) · pp. 304–316

DOI
10.20956/j.v19i2.23263
ISSN
2614-8811, 1858-1382
Published
2023-01-05
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

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.

Bahasa Indonesia

Bilangan Trinion dan Quaternion adalah salah satu dari bilangan hypercomplex yang merupakan perluasan dari bilangan complex. Dari bilangan Trinion dan Quaternion dapat terbentuk suatu bimodul yang merupakan pasangan terurut dari Trinion dan Quaternion. Selanjutnya, bilangan Trinion, Quaternion dan bimodulnya dikemas kedalam bentuk Matriks Segitiga Formal yang berordo. Matriks Segitiga Formal lebih dikenal sebagai Matriks Segitiga Atas. Dikarenakan bilangan Trinion, Quaternion dan bimodulnya merupakan gelanggang, maka Matriks Segitiga Formal tersebut dapat disebut Gelanggang Matriks Segitiga Formal. Tujuan dari penelitian ini ialah untuk mengkonstruksi Gelanggang Armendariz menggunakan Gelanggang Matriks Segitiga Formal. Hasil yang akan diperoleh menunjukkan bahwa Gelanggang Matriks Segitiga Formal merupakan Gelanggang -Skew Armendariz dan Gelanggang -Skew -Armendariz, dimana adalah endomorfisma Gelanggang Matriks Segitiga Formal dan adalah derivatif. Kata kunci: Trinion, Quaternion, Bimodul, Gelanggang Matriks Segitiga Formal, Gelanggang Armendariz

Keywords

Collaboration network of the authors

29 authors · 52 co-authorship links · 1 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Hasanuddin University
  • Telkom University
  • Universitas Halu Oleo
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Nur ErawatiAffiliation unknown2
Hasmawati HasmawatiTelkom University2
winda aritonangAffiliation unknown2
Jeriko GormantaraAffiliation unknown1
Hanni GarminiaAffiliation unknown1
Evan RamdanAffiliation unknown1
Loeky HaryantoAffiliation unknown1
Fauziah BaharuddinAffiliation unknown1
Afriani AfrianiAffiliation unknown1
Qharnida KharianiAffiliation unknown1
Hasmawati BasirAffiliation unknown1
Armin LawiHasanuddin University1
Nurhidayah NurhidayahUniversitas Halu Oleo1
Supri AmirHasanuddin University1
Edy SaputraHasanuddin University1
Mawardi BahriAffiliation unknown1
Yudhiyanto SupriadiAffiliation unknown1
Budi NurwahyuAffiliation unknown1
Ahmad Syukur DamingAffiliation unknown1
Ali AhmadAffiliation unknown1
Jusmawati JusmawatiAffiliation unknown1
St. Munieroh FachrunnisaAffiliation unknown1
Andi Muhammad AnwarAffiliation unknown1
Jeki SaputraAffiliation unknown1
Nurhafizah NurhafizahAffiliation unknown1
Nur ErawatyAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">The Construction of Armendariz Ring using Formal Triangle Matrix Ring</dc:title>
	<dc:title xml:lang="id">Konstruksi Gelanggang Armendariz menggunakan Gelanggang Matriks Segitiga Formal</dc:title>
	<dc:creator xml:lang="en">Anwar, Aidah Nabilah</dc:creator>
	<dc:creator xml:lang="en">Amir, Amir Kamal</dc:creator>
	<dc:creator xml:lang="en">Hinding, Nurdin</dc:creator>
	<dc:subject xml:lang="en">Trinion</dc:subject>
	<dc:subject xml:lang="en">Quaternion</dc:subject>
	<dc:subject xml:lang="en">BImodule</dc:subject>
	<dc:subject xml:lang="en">Ring</dc:subject>
	<dc:subject xml:lang="en">Formal Triangle Matrix Ring</dc:subject>
	<dc:subject xml:lang="en">Armendariz Ring</dc:subject>
	<dc:subject xml:lang="id">Trinion</dc:subject>
	<dc:subject xml:lang="id">quaternion</dc:subject>
	<dc:subject xml:lang="id">Bimodul</dc:subject>
	<dc:subject xml:lang="id">Gelanggang</dc:subject>
	<dc:subject xml:lang="id">Gelanggang Matriks Segitiga Formal</dc:subject>
	<dc:subject xml:lang="id">Gelanggang Armendariz</dc:subject>
	<dc:description xml:lang="en">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.</dc:description>
	<dc:description xml:lang="id">Bilangan Trinion dan Quaternion adalah salah satu dari bilangan hypercomplex yang merupakan perluasan dari bilangan complex. Dari bilangan Trinion dan Quaternion dapat terbentuk suatu bimodul yang merupakan pasangan terurut dari Trinion dan Quaternion. Selanjutnya, bilangan Trinion, Quaternion dan bimodulnya dikemas kedalam bentuk Matriks Segitiga Formal yang berordo . Matriks Segitiga Formal lebih dikenal sebagai Matriks Segitiga Atas. Dikarenakan bilangan Trinion, Quaternion dan bimodulnya merupakan gelanggang, maka Matriks Segitiga Formal tersebut dapat disebut Gelanggang Matriks Segitiga Formal. Tujuan dari penelitian ini ialah untuk mengkonstruksi Gelanggang Armendariz menggunakan Gelanggang Matriks Segitiga Formal. Hasil yang akan diperoleh menunjukkan bahwa Gelanggang Matriks Segitiga Formal merupakan Gelanggang -Skew Armendariz dan Gelanggang -Skew -Armendariz, dimana &amp;nbsp;adalah endomorfisma Gelanggang Matriks Segitiga Formal dan &amp;nbsp;adalah &amp;nbsp;derivatif.
Kata kunci : Trinion, Quaternion, Bimodul, Gelanggang Matriks Segitiga Formal, Gelanggang Armendariz</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2023-01-05</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/23263</dc:identifier>
	<dc:identifier>10.20956/j.v19i2.23263</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 19 No. 2 (2023): JANUARY 2023; 304-316</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/23263/9151</dc:relation>
	<dc:relation>10.20956/j.v19i2.23263.g9151</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2023 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>