Research On Strongly Copure Projectivity

In this thesis,we mainly study strongly copure projective objects and their homological properties in categories of modules and extriangulated categories with IE-triangles proper class ξ and enough ξ-projectives(injectives),which consists of two parts.Firstly,we discuss the retention of strongly copure projectivity under ring ex-tensions,such as excellent extensions,Frobenius extensions,localized extensions.Secondly,we introduce the ξ-strongly copure projective objects in extriangu-lated categories,and study some basic homological properties of ξ-strongly cop-ure projective objects.We also prove that the class of strongly copure projec-tive objects is closed finite direct sums,direct summands.and for any IE-triangle(?)in ξ,if C is ξ-strongly copure projective objects,then B is ξ-strongly copure projective objects if and only if B is ξ-strongly copure projec-tive objects.and we show the ξ-strongly copure projective dimension of object A in extriangulated categories at most n if and only if for any ξ-exact complex B’→P’n-1→P’n-2→…→P’0→A.If each Pi is ξ-strongly copure projective object,then so is B.