Some variations of projectivity

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dc.authorscopusid23994847400en_US
dc.contributor.authorErtaş, Nil Orhan
dc.contributor.authorTribak, Rachid
dc.date.accessioned2022-04-21T05:40:13Z
dc.date.available2022-04-21T05:40:13Z
dc.date.issued2022en_US
dc.departmentBTÜ, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractWe prove that a ring R has a module M whose domain of projectivity consists of only some injective modules if and only if R is a right noetherian right V-ring. Also, we consider modules which are projective relative only to a subclass of max modules. Such modules are called max-poor modules. In a recent paper Holston et al. showed that every ring has a p-poor module (that is a module whose projectivity domain consists precisely of the semisimple modules). So every ring has a max-poor module. The structure of all max-poor abelian groups is completely determined. Examples of rings having a max-poor module which is neither projective nor p-poor are provided. We prove that the class of max-poor R-modules is closed under direct summands if and only if R is a right Bass ring. A ring R is said to have no right max-p-middle class if every right R-module is either projective or max-poor. It is shown that if a commutative noetherian ring R has no right max-p-middle class, then R is the ring direct sum of a semisimple ring R1 and a ring R2 which is either zero or an artinian ring or a one-dimensional local noetherian integral domain such that the quotient field Q2 of R2 has a proper R2-submodule which is not complete in its R2-Topology. Then we show that a commutative noetherian hereditary ring R has no right max-p-middle class if and only if R is a semisimple ringen_US
dc.identifier.doi10.1142/S021949882250236Xen_US
dc.identifier.issn02194988
dc.identifier.issue12
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12885/1908
dc.identifier.volume21
dc.indekslendigikaynakScopusen_US
dc.institutionauthorErtaş, Nil Orhan
dc.language.isoenen_US
dc.publisherWorld Scientificen_US
dc.relation.ispartofJournal of Algebra and its Applicationsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectInjective moduleen_US
dc.subjectmax moduleen_US
dc.subjectmax-poor moduleen_US
dc.subjectp-poor moduleen_US
dc.subjectprojective moduleen_US
dc.subjectprojectivity domainen_US
dc.subjectright Bass ringen_US
dc.titleSome variations of projectivityen_US
dc.typeArticleen_US

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