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Homoderivations in Prime Near Rings

Jurnal Matematika, Statistika dan Komputasi · Vol. 23 No. 1 (2026) · hlm. 49–58

DOI
10.20956/zsw81k91
ISSN
2614-8811, 1858-1382
Terbit
2026-09-15
Penerbit
Department of Mathematics, Hasanuddin University
Bahasa
en
Lisensi
creativecommons.org/licenses/by/4.0

Abstrak

Homoderivations represent a generalized differential operator that combines multiplicative and derivational properties, making them significant in studying algebraic structures with hybrid operations. This paper initiates the systematic study of homoderivations on prime near rings, an algebraic structure where only left distributivity holds. We establish the foundational Leibniz formula and investigate when the existence of such mapping forces the underlying near ring to become commutative. Specificall, we prove that if a 2-torsion free prime near ring admits a non zero homoderivation h with h([x,y])=0 or h(x◦y)=0, then N is a commutative ring. Furthermore, we characterize the center of the near ring through the behavior of homoderivations on square closed Lie ideals. These results have implications for understanding the interplay between ring theoritic derivation and multiplicative mappings in non ring.

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6 penulis · 11 tautan kepenulisan bersama · 8 lintas organisasi

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  • Universitas Ahmad Dahlan
  • Universitas Gadjah Mada
  • Bandung Institute of Technology
  • Diponegoro University
  • Organisasi berbeda
  • Organisasi sama
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Rekan penulisOrganisasiArtikel bersama
Dian Ariesta YuwaningsihUniversitas Ahmad Dahlan1
Yassin Dwi CahyoDiponegoro University1
Rima Aksen CahdriyanaUniversitas Ahmad Dahlan1
Dea AprianiUniversitas Ahmad Dahlan1

Afiliasi berasal dari OpenAlex; metadata OAI-PMH jurnal tidak memuatnya. Penulis tanpa ID OpenAlex dicocokkan berdasarkan nama, sehingga dua orang bisa tergabung atau satu orang bisa terpisah.

Sumber metadata: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, pertama di-harvest 5 Nov 2026, terakhir terlihat 5 Nov 2026.
Metadata asli (oai_dc) 
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	<dc:title xml:lang="en">Homoderivations in Prime Near Rings</dc:title>
	<dc:creator xml:lang="en">Yanti, Gusti Ayu Dwi</dc:creator>
	<dc:creator xml:lang="en">Saruan, Sandy Salomo</dc:creator>
	<dc:subject xml:lang="en">homoderivation</dc:subject>
	<dc:subject xml:lang="en">prime near ring</dc:subject>
	<dc:subject xml:lang="en">commutativity theorem</dc:subject>
	<dc:subject xml:lang="en">Lie structure</dc:subject>
	<dc:subject xml:lang="en">Derivation</dc:subject>
	<dc:subject xml:lang="en">Ring</dc:subject>
	<dc:description xml:lang="en">Homoderivations represent a generalized differential operator that combines multiplicative and derivational properties, making them significant in studying algebraic structures with hybrid operations. This paper initiates the systematic study of homoderivations on prime near rings, an algebraic structure where only left distributivity holds. We establish the foundational Leibniz formula and investigate when the existence of such mapping forces the underlying near ring to become commutative. Specificall, we prove that if a 2-torsion free prime near ring admits a non zero homoderivation h&amp;nbsp;with h([x,y])=0&amp;nbsp;or h(x◦y)=0, then N&amp;nbsp;is a commutative ring. Furthermore, we characterize the center of the near ring through the behavior of homoderivations on square closed Lie ideals. These results have implications for understanding the interplay between ring theoritic derivation and multiplicative mappings in non ring.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2026-09-15</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:type xml:lang="en">text</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/52060</dc:identifier>
	<dc:identifier>10.20956/zsw81k91</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 23 No. 1 (2026): September 2026; 49-58</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/52060/15003</dc:relation>
	<dc:coverage xml:lang="en">Ring theory</dc:coverage>
	<dc:rights xml:lang="en">Copyright (c) 2026 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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