Direct Sums Of Cofinitely H-Supplemented Modules And Goldie~*-Supplemented Modules

This dissertation consists of four chapters. In Chapter 1, we illustrate thebackground of modules'development, the important roles of the module's theoryin the process of algebra and the progress related to H-supplemented modules andGoldie*-supplemented modules. In Chapter 2, some basic de?nitions and importantlemmas related to this paper are given. In Chapter 3, an equivalent characterizationof co?nitely H-supplemented modules is given by the (β|ˉ) relation, it is shown thatM = M₁⊕M₂ be a co?nitely supplemented module, if M₁ is M₂-sjective(or M2is M₁-sjective) and M1 and M₂ are cofnitely H-supplemented, then M is co?nitelyH-supplemented. In Chapter 4, direct sums and summands of Goldie*-supplementedmodules are discussed. It is proved that Goldie*-supplemented modules M1 and M2such that M = M1⊕M2, if M1 is M2-sjective(or M2 is M1-sjective), then M is aGoldie*-supplemented module.