Morfizmalar Yardımıyla Tanımlanan Bazı Halka ve Modül Yapıları

Abstract

Let M ve N be R-modules. Recent works have shown that some structures of the ring and module theory can be carried out in the context of Hom(M,N), the abelian group of all morphisms of M into N. The aim of this thesis is to investigate some ring and module structures defined by morphisms. The introductory chapter consists of informations about the importance and the historical improvement of the thesis subject. The second chapter contains introductory information needed for the thesis. In the third chapter of the thesis, substructures of Hom(M,N) such as the total,the radical, the singular ideal and the co-singular ideal are examined and these substructures are carried out to the category of modules. Then locally injective and locally projective modules are introduced and these modules are characterized by the singular ideal, the co-singular ideal and the total. In the last chapter, the definition of a regular element for a ring and a module is generalized to module homomorphisms.