(n,0)-Projective Dimensions And (n,0)-Injective Covers

The subject of relative homological algebra was introduced by S.Eilenberg and J.C.Moore in 1965.The research about the subject largely developed and extended the classical results about homological algebra.The theory of relative homological dimensions of modules and rings are the main research field in the subject.The existence of covers and envelopes,which introduced by Enochs in 1981,are basic researching objects of the subject.This thesis consists of three chapters.In chapter one,we recall some notions,backgrounds and facts needed in the sequel,and list the main results of this thesis.In chapter two,we first give a characterization of n-presented module. Then we introduce the concept of(n,0)-projective dimension for modules and rings.It measures how far away a finitely generated module is from being n-presented,and how far away a ring is from being Noetherian.Various characterizations of the dimension are given.In chapter three,we show that if R is a right n-coherent ring,then every right R-module has an(n,0)-injective(pre)cover.As applications of the previous result,we give some characterizations of(n,0)-rings,von Neumann regular rings and semisimple rings.Finally,a question and a conjecture are given.