Browsing by Author "Durgun, Yilmaz"

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    Small supplements weak supplements and proper classes
    (Hacettepe Univ, FAC Sci, 2016) Engin BÜYÜKAŞIK; Rafail ALİZADE; Yılmaz DUR?GUN; Buyukasik, Engin; Durgun, Yilmaz; Alizade, Rafail; Dur?gun, Yılmaz
    Let SS denote the class of short exact sequences E :0 ->, A->, 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 suchthat 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 classSS coincides with the smallest proper class containing the class of short exact sequences determined by weak supplementsubmodules. The homological objects such as SS-projective and SScoinjective modules are investigated. In order to describe the classSS we investigate small supplemented modules i.e. the modules each ofwhose submodule has a small supplement. Besides proving some closure properties of small supplemented modules we also give a completecharacterization of these modules over Dedekind domains