Alizade, RafailDemirci, Yılmaz MehmetAlizade, Rafail04.02. Department of Mathematics04. Faculty of Science01. Izmir Institute of Technology2014-07-222014-07-222008https://hdl.handle.net/11147/3956Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2008Includes bibliographical references (leaves: 37-38)Text in English: Abstract: Turkish and Englishix, 40 leavesIn this thesis, we study the class S of all short exact sequences 0 A B C 0 where Im& has a supplement in B, i.e. a minimal elemenr in the set {V B V + Im& . B}.The corresponding elements of ExtR(C;A) are called k-elements. In general k-elements need not form a subgroup in ExtR(C;A), but in the category TR of torsion R-modules over a Dedekind domain R, S is a proper class; there are no nonzero S-projective modules and the only S-injective modules are injective R-modules in TR. In this thesis we also give the structure of S-coinjective R-modules in TR. Moreover, we define the class SB of all short exact sequences 0 A B C 0 where Im & has a supplement V in B and V in B and In & is bounded. The corresponding elements of ExtR(C;A) are called B-elements. Over a noetherian integral domain of Krull dimension 1, B-elements form a proper class. In the category TR over a Dedekind domain R, SB is a proper class; there are no nonzero SB-projective R-modules and SB-injective R-modules are only the injective R-modules. In the category TR, reduced SB-coinjective R-modules are bounded R-modules.eninfo:eu-repo/semantics/openAccessQA247. D378 2008Modules (Algebra)Master Thesis