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dc.contributor.authorAlizade, Rafail
dc.contributor.authorBüyükaşık, Engin
dc.contributor.authorDurğun, Yılmaz
dc.date.accessioned2017-06-28T12:55:21Z
dc.date.available2017-06-28T12:55:21Z
dc.date.issued2016
dc.identifier.citationAlizade, R., Büyükaşık, E., and Durğun, Y. (2016). Small supplements, weak supplements and proper classes. Hacettepe Journal of Mathematics and Statistics, 45(3), 649-661. doi:10.15672/HJMS.20164512507en_US
dc.identifier.issn1303-5010
dc.identifier.urihttp://hdl.handle.net/11147/5798
dc.description.abstractLet SS denote the class of short exact sequences E:0 → Af→ B → C → 0 of R-modules and R-module homomorphisms such that f(A) has a small supplement in B i.e. there exists a submodule K of M such that f(A) + K = B and f(A) ∩ K is a small module. It is shown that, SS is a proper class over left hereditary rings. Moreover, in this case, the proper class SS coincides with the smallest proper class containing the class of short exact sequences determined by weak supplement submodules. The homological objects, such as, SS-projective and SScoinjective modules are investigated. In order to describe the class SS, we investigate small supplemented modules, i.e. the modules each of whose submodule has a small supplement. Besides proving some closure properties of small supplemented modules, we also give a complete characterization of these modules over Dedekind domains.en_US
dc.language.isoengen_US
dc.publisherHacettepe Üniversitesien_US
dc.relation.isversionof10.15672/HJMS.20164512507en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectSmall moduleen_US
dc.subjectGeneral module theoryen_US
dc.subjectHomological functors on modulesen_US
dc.subjectProper class of short exact sequencesen_US
dc.subjectCommutative ringsen_US
dc.titleSmall supplements, weak supplements and proper classesen_US
dc.typearticleen_US
dc.contributor.authorIDTR130906en_US
dc.contributor.iztechauthorBüyükaşık, Engin
dc.relation.journalHacettepe Journal of Mathematics and Statisticsen_US
dc.contributor.departmentİYTE, Fen Fakültesi, Matematik Bölümüen_US
dc.identifier.volume45en_US
dc.identifier.issue3en_US
dc.identifier.startpage649en_US
dc.identifier.endpage661en_US
dc.identifier.wosWOS:000384774500001
dc.identifier.scopusSCOPUS:2-s2.0-84978698431
dc.relation.publicationcategoryMakale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanıen_US


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