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THE CLEANNESS OF THE SUBRINGS OF M_2 (Z_P)

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 18 No. 2 (2024) · pp. 1307–1316

DOI
10.30598/barekengvol18iss2pp1307-1316
ISSN
2615-3017, 1978-7227
Published
2024-05-25
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

Let be a ring. Ring is said to be a clean ring if every element of R can be expressed as the sum of a unit and an idempotent element. Furthermore, there are r-clean rings. An r-clean ring is a generalization of a clean ring. In an r-clean ring, all of its elements can be represented as the sum of a regular element and an idempotent element. Moreover, strongly r-clean rings were introduced. A strongly r-clean ring is a ring where every element of the ring can be expressed as the sum of a regular and an idempotent element, and the multiplication of that regular and idempotent is commutative. On the other hand, there is a ring of the set of matrices over ring denotes by. In this paper, we will discuss the cleanness properties, especially strongly r-clean of the subring of. The aims of this paper are to find the characteristics of strongly r-clean of the subring of. Here, we assumed that is a ring of matrix over.

Collaboration network of the authors

10 authors · 21 co-authorship links · 8 across different organisations

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

  • Diponegoro University
  • Universitas Gadjah Mada
  • Universitas Sulawesi Barat
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Meryta Febrilian FatimahUniversitas Sulawesi Barat1
Fitriana HasnaniUniversitas Gadjah Mada1
Suffi NuralesaDiponegoro University1
Galang Riki RamadhanDiponegoro University1
Carolus Pasha Lazuardi Jituprasojo HatmakelanaUniversitas Gadjah Mada1
Nurul FadhilahDiponegoro University1
Benediktus Panji PradiptaDiponegoro University1

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://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 8 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en-US">THE CLEANNESS OF THE SUBRINGS OF M_2 (Z_P)</dc:title>
	<dc:creator>Alfiana, Shinta Nur</dc:creator>
	<dc:creator>Puspita, Nikken Prima</dc:creator>
	<dc:creator>Widowati, Widowati</dc:creator>
	<dc:description xml:lang="en-US">Let &amp;nbsp;be a ring. Ring &amp;nbsp;is said to be a clean ring if every element of R can be expressed as the sum of a unit and an idempotent element. Furthermore, there are r-clean rings. An r-clean ring is a generalization of a clean ring. In an r-clean ring, all of its elements can be represented as the sum of a regular element and an idempotent element.&amp;nbsp; Moreover, strongly r-clean rings were introduced. A strongly r-clean ring is a ring where every element of the ring can be expressed as the sum of a regular and an idempotent element, and the multiplication of that regular and idempotent is commutative. On the other hand, there is a ring of the set of matrices over ring &amp;nbsp;denotes by . In this paper, we will discuss the cleanness properties, especially strongly r-clean of the subring of . The aims of this paper are to find the characteristics of strongly r-clean of the subring of . Here, we assumed that &amp;nbsp;is a ring of matrix over .</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2024-05-25</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://ojs3.unpatti.ac.id/index.php/barekeng/article/view/12360</dc:identifier>
	<dc:identifier>10.30598/barekengvol18iss2pp1307-1316</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application; 1307-1316</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol18iss2year2024</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/12360/7945</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2024 Shinta Nur Alfiana, Nikken Prima Puspita, Widowati Widowati</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
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