Min-pure-projective And CI-projective Modules

In this paper, we mainly study the min-pure-projective and CI-projective mod-ules, and we study the concept of dual notions min-pure-injective and CI-injectivemodules. Then we discuss the basic characterizations of them. We obtain the rela-tion of min-injective (min-flat) modules and min-pure-injective (min-pure-flat) mod-ules. Also we define and investigate CI-projective dimensions and CI-injective di-mensions, and prove the class of CI-projective modules and the right orthogonalclass of them is a hereditary cotorsion theory.