Algebraic Structure Of The Cohomology

In this thesis, we study the cohomology of some algebraic strutures. It can be divided into four chapters:In the first chapter, there is a brief introduction. The developing background of our subject in this paper is given.In the second chapter, We provide some basic concepts and necessary results which will be used in this paper.In the third chapter, we study the cohomology of objects of finiteξ—(?) projective dimension. Insection 1, the relative cohomology is introduced in triangulated categories. In section 2, the tight connections between the three cohomology theories are established in triangulated categories.In the fourth chapter, we study the cohomology structure of coring. In section 1, some basic concepts and examples about coring are introduced. In section 2, we construct the cochain complex Cc(A, M) associated to an A—coring C and an A—bimodule M. Using it we can give the module valued cohomology of a coring. As an application, we analyse its structure in the case of the canonical coring. Finally, the construction of the previous section can be dualised to produce a cohomology of a C—ring.