On simple-injective modules
| dc.authorid | alagoz, yusuf/0000-0002-2535-4679 | |
| dc.contributor.author | Alagoz, Yusuf | |
| dc.contributor.author | Benli-Goral, Sinem | |
| dc.contributor.author | Buyukasik, Engin | |
| dc.date.accessioned | 2024-12-24T19:29:44Z | |
| dc.date.available | 2024-12-24T19:29:44Z | |
| dc.date.issued | 2023 | |
| dc.department | Siirt Üniversitesi | |
| dc.description.abstract | For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for every cyclic right module N. The rings whose simple-injective right modules are injective are exactly the right Artinian rings. A right Noetherian ring is right Artinian if and only if every cyclic simple-injective right module is injective. The ring is QF if and only if simple-injective right modules are projective. For a commutative Noetherian ring R, we prove that every finitely generated simple-injective R-module is projective if and only if R = A x B, where A is QF and B is hereditary. An abelian group is simple-injective if and only if its torsion part is injective. We show that the notions of simple-injective, strongly simple-injective, soc-injective and strongly soc-injective coincide over the ring of integers. | |
| dc.identifier.doi | 10.1142/S0219498823501384 | |
| dc.identifier.issn | 0219-4988 | |
| dc.identifier.issn | 1793-6829 | |
| dc.identifier.issue | 6 | |
| dc.identifier.scopus | 2-s2.0-85129012004 | |
| dc.identifier.scopusquality | Q2 | |
| dc.identifier.uri | https://doi.org/10.1142/S0219498823501384 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12604/7226 | |
| dc.identifier.volume | 22 | |
| dc.identifier.wos | WOS:000849402000003 | |
| dc.identifier.wosquality | Q3 | |
| dc.indekslendigikaynak | Web of Science | |
| dc.indekslendigikaynak | Scopus | |
| dc.language.iso | en | |
| dc.publisher | World Scientific Publ Co Pte Ltd | |
| dc.relation.ispartof | Journal of Algebra and Its Applications | |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/closedAccess | |
| dc.snmz | KA_20241222 | |
| dc.subject | (Min) injective modules | |
| dc.subject | simple-injective modules | |
| dc.subject | Artinian rings | |
| dc.title | On simple-injective modules | |
| dc.type | Article |
