Cotorsion Pair And Cotiling Module

In chapter one,the development of algebra and the research present situation of homology dimension and tilting theory is introduced.In chapter two,a new characterization of Gorenstein injective module is given.Ifis a ring,then it is proven thatis a Gorenstein injective module if and only if there is a strongly Gorenstein left-R injective modulesuch that M∈(~⊥N)~⊥andis pure module.In chapter three,some sufficient conditions when the kernel of a complete hereditary cotorsion pair is the direct summand of direct products of a cotilting module are given by studying the properties of the cotorsion pair and cotilting modules.In chapter four,FC-projective complexes are introduced and studied.Furthermore,the definition of Gorenstein FC-projective complexes is given,and some properties of Gorenstein FC-projective complexes are studied.