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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) · hlm. 1307–1316

DOI
10.30598/barekengvol18iss2pp1307-1316
ISSN
2615-3017, 1978-7227
Terbit
2024-05-25
Penerbit
PATTIMURA UNIVERSITY
Bahasa
eng
Lisensi
creativecommons.org/licenses/by-sa/4.0

Abstrak

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.

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10 penulis · 21 tautan kepenulisan bersama · 8 lintas organisasi

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  • Diponegoro University
  • Universitas Gadjah Mada
  • Universitas Sulawesi Barat
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Rekan penulisOrganisasiArtikel bersama
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

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Sumber metadata: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/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-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>
</oai_dc:dc>