On Purities Relative to Minimal Right Ideals
| dc.contributor.author | Alagoz, Yusuf | |
| dc.contributor.author | Alizade, Rafail | |
| dc.contributor.author | Buyukasik, Engin | |
| dc.contributor.author | Sagbas, Selcuk | |
| dc.date.accessioned | 2024-12-24T19:29:38Z | |
| dc.date.available | 2024-12-24T19:29:38Z | |
| dc.date.issued | 2023 | |
| dc.department | Siirt Üniversitesi | |
| dc.description.abstract | We call a right module M weakly neat-flat if Hom(S, N) -> Hom(S, M) is surjective for any epimorphism N -> M and any simple right ideal S. A left module M is called weakly absolutely s-pure if S circle times M -> S circle times N is monic, for any monomorphism M -> N and any simple right ideal S. These notions are proper generalization of the neat-flat and the absolutely s-pure modules which are defined in the same way by considering all simple right modules of the ring, respectively. In this paper, we study some closure properties of weakly neat-flat and weakly absolutely s-pure modules, and investigate several classes of rings that are characterized via these modules. The relation between these modules and some well-known homological objects such as projective, flat, injective and absolutely pure are studied. For instance, it is proved that R is a right Kasch ring if and only if every weakly neat-flat right R-module is neat-flat (moreover if R is right min-coherent) if and only if every weakly absolutely s-pure left R-module is absolutely s-pure. The rings over which every weakly neat-flat (resp. weakly absolutely s-pure) module is injective and projective are exactly the QF rings. Finally, we study enveloping and covering properties of weakly neat-flat and weakly absolutely s-pure modules. The rings over which every simple right ideal has an epic projective envelope are characterized. | |
| dc.identifier.doi | 10.1134/S1995080223070053 | |
| dc.identifier.endpage | 2566 | |
| dc.identifier.issn | 1995-0802 | |
| dc.identifier.issn | 1818-9962 | |
| dc.identifier.issue | 7 | |
| dc.identifier.scopus | 2-s2.0-85175205511 | |
| dc.identifier.scopusquality | Q2 | |
| dc.identifier.startpage | 2557 | |
| dc.identifier.uri | https://doi.org/10.1134/S1995080223070053 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12604/7185 | |
| dc.identifier.volume | 44 | |
| dc.identifier.wos | WOS:001098734800004 | |
| dc.identifier.wosquality | Q2 | |
| dc.indekslendigikaynak | Web of Science | |
| dc.indekslendigikaynak | Scopus | |
| dc.language.iso | en | |
| dc.publisher | Maik Nauka/Interperiodica/Springer | |
| dc.relation.ispartof | Lobachevskii Journal of Mathematics | |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | |
| dc.rights | info:eu-repo/semantics/closedAccess | |
| dc.snmz | KA_20241222 | |
| dc.subject | (weakly) neat-flat modules | |
| dc.subject | (weakly) absolutely s-pure modules | |
| dc.subject | Auslander-Bridger transpose | |
| dc.subject | Kasch rings | |
| dc.title | On Purities Relative to Minimal Right Ideals | |
| dc.type | Article |
