Homoderivations in Prime Near Rings

Yanti, Gusti Ayu Dwi; Saruan, Sandy Salomo

doi:10.20956/zsw81k91

Open access Journal

Homoderivations in Prime Near Rings

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

DOI: 10.20956/zsw81k91
ISSN: 2614-8811, 1858-1382
Published: 2026-09-15
Publisher: Department of Mathematics, Hasanuddin University
Language: en
License: creativecommons.org/licenses/by/4.0

Abstract

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.

Keywords

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Co-author	Organisation	Joint articles
Dian Ariesta Yuwaningsih	Affiliation unknown	1
Yassin Dwi Cahyo	Affiliation unknown	1
Rima Aksen Cahdriyana	Affiliation unknown	1
Dea Apriani	Affiliation unknown	1

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">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>
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	<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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