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 ? and enough ?-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 ?-strongly copure projective objects in extriangu-lated categories,and study some basic homological properties of ?-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 ?,if C is ?-strongly copure projective objects,then B is ?-strongly copure projective objects if and only if B is ?-strongly copure projec-tive objects.and we show the ?-strongly copure projective dimension of object A in extriangulated categories at most n if and only if for any ?-exact complex B'?P'n-1?P'n-2?�?P'0?A.If each Pi is ?-strongly copure projective object,then so is B.