Modules and abelian groups with a bounded domain of injectivity
| dc.authorid | Demirci, Yilmaz Mehmet/0000-0003-3802-4211 | |
| dc.contributor.author | Demirci, Yilmaz Mehmet | |
| dc.date.accessioned | 2025-03-23T19:31:02Z | |
| dc.date.available | 2025-03-23T19:31:02Z | |
| dc.date.issued | 2018 | |
| dc.department | Sinop Üniversitesi | |
| dc.description.abstract | In this work, impecunious modules are introduced as modules whose injectivity domains are contained in the class of all pure-split modules. This notion gives a generalization of both poor modules and pure-injectively poor modules. Properties involving impecunious modules as well as examples that show the relations between impecunious modules, poor modules and pure-injectively poor modules are given. Rings over which every module is impecunious are right pure-semisimple. A commutative ring over which there is a projective semisimple impecunious module is proved to be semisimple artinian. Moreover, the characterization of impecunious abelian groups is given. It states that an abelian group M is impecunious if and only if for every prime integer p, M has a direct summand isomorphic to Z(p)(n) for some positive integer n. Consequently, an example of an impecunious abelian group which is neither poor nor pure-injectively poor is given so that the generalization defined is proper. | |
| dc.identifier.doi | 10.1142/S0219498818501086 | |
| dc.identifier.issn | 0219-4988 | |
| dc.identifier.issn | 1793-6829 | |
| dc.identifier.issue | 6 | |
| dc.identifier.scopusquality | Q2 | |
| dc.identifier.uri | https://doi.org/10.1142/S0219498818501086 | |
| dc.identifier.uri | https://hdl.handle.net/11486/5201 | |
| dc.identifier.volume | 17 | |
| dc.identifier.wos | WOS:000433001200011 | |
| dc.identifier.wosquality | Q3 | |
| dc.indekslendigikaynak | Web of Science | |
| dc.institutionauthor | Demirci, Yilmaz Mehmet | |
| 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_WOS_20250323 | |
| dc.subject | Poor module | |
| dc.subject | pure-injectively poor module | |
| dc.subject | impecunious module | |
| dc.subject | pure-split module | |
| dc.subject | impecunious abelian group | |
| dc.title | Modules and abelian groups with a bounded domain of injectivity | |
| dc.type | Article |
