THE SOURCE OF SEMIPRIMENESS OF RINGS
| dc.authorid | Demir, Cagri/0000-0003-0662-9494 | |
| dc.contributor.author | Aydin, Neset | |
| dc.contributor.author | Demir, Cagri | |
| dc.contributor.author | Camci, Didem Karalarlioglu | |
| dc.date.accessioned | 2025-01-27T21:19:57Z | |
| dc.date.available | 2025-01-27T21:19:57Z | |
| dc.date.issued | 2018 | |
| dc.department | Çanakkale Onsekiz Mart Üniversitesi | |
| dc.description.abstract | Let R be an associative ring. We define a subset S-R of R as S-R = {a is an element of R vertical bar aRa = (0)} and call it the source of semiprimeness of R. We first examine some basic properties of the subset S-R in any ring R, and then define the notions such as R being a vertical bar S-R vertical bar-reduced ring, a vertical bar S-R vertical bar-domain and a vertical bar S-R vertical bar-division ring which are slight generalizations of their classical versions. Beside others, we for instance prove that a finite vertical bar S-R vertical bar-domain is necessarily unitary, and is in fact a vertical bar S-R vertical bar-division ring. However, we provide an example showing that a finite vertical bar S-R vertical bar-division ring does not need to be commutative. All possible values for characteristics of unitary vertical bar S-R vertical bar-reduced rings and vertical bar S-R vertical bar-domains are also determined. | |
| dc.identifier.doi | 10.4134/CKMS.c170409 | |
| dc.identifier.endpage | 1096 | |
| dc.identifier.issn | 1225-1763 | |
| dc.identifier.issn | 2234-3024 | |
| dc.identifier.issue | 4 | |
| dc.identifier.scopus | 2-s2.0-85056526802 | |
| dc.identifier.scopusquality | Q3 | |
| dc.identifier.startpage | 1083 | |
| dc.identifier.uri | https://doi.org/10.4134/CKMS.c170409 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12428/28782 | |
| dc.identifier.volume | 33 | |
| dc.identifier.wos | WOS:000449061700004 | |
| dc.identifier.wosquality | N/A | |
| dc.indekslendigikaynak | Web of Science | |
| dc.indekslendigikaynak | Scopus | |
| dc.language.iso | en | |
| dc.publisher | Korean Mathematical Soc | |
| dc.relation.ispartof | Communications of The Korean Mathematical Society | |
| dc.relation.publicationcategory | info:eu-repo/semantics/openAccess | |
| dc.rights | info:eu-repo/semantics/closedAccess | |
| dc.snmz | KA_WoS_20250125 | |
| dc.subject | prime ideal | |
| dc.subject | semiprime ideal | |
| dc.subject | prime ring and semiprime ring | |
| dc.title | THE SOURCE OF SEMIPRIMENESS OF RINGS | |
| dc.type | Article |
