Generalized Projection Mode

Gorenstein projective, injective and flat modules have been studied by many authors. In recent years, Gorenstein homological algebra has become a vigorously active area of research, and various generalizations of Gorenstein homological modules have been intro-duced and researched. For example, more recently, Ding introduced a concept of Ding projective modules which have nice propertiesIn this paper, we first give the nation of generally Ding projective module. An R-module M is called generally Ding projective module if there is an exact sequence …â†' F1â†'F0â†'F0â†'F1â†'… of flat R-modules with M≌im(F0â†'F0) such that Hom(-,F) leaves the sequence exact whenever F is a flat R-module.In order to have a better study of generally Ding projective modules, We define a new ring which is called weak perfect ring. There are a variety of nice results about generally Ding projective modules over weak perfect ring. The main purpose of this paper is to introduce and study the resolving properties of the class of generally Ding projective modules and the existence of generally Ding projective precovers and the general Ding projective dimension.