The Study Of Gorenstein Modules

Gorenstein homological modules have an extreme important effects to ho-mological algebra. The theory of homological modules was first studied by Enochs as a special module and indicate that a module M is injective (pro-jective) if and only if Gorenstein injective (projective) module. Gorenstein dimensions were studied by many scholars, the properties of Gorenstein di-mensions are so important and perfect in homological theory, so is the injective (flat) module.(n,m)-strongly Gorenstein injective modules were mainly studied in the second chapter of the article and the cosyzygy is (n, m-i)-strongly Gorenstein injective modules were alao obtained.(n,m)-strongly Gorenstein flat modules were mainly discussed in the third chapter of the article. The (n,m)-strongly Gorenstein flat module was defined. The properties of the (n,m)-strongly Gorenstein flat module were studied on the basis of its definition.Gorenstein injective syzygy module and its property were studied in the fourth chapter, we first give the definition of Gorenstein injective syzygy mod-ule. If there exist complex…→G1→G0→M→0, with Gi Goren-stein injective module, let A=Kn=Ker(Gn-1→Gn-2), we called A is the Gorenstein n-injective module of M. and when R is n-Gorenstein ring, module M is Gorenstein injective module if there is an exact sequence 0→A→G1→G0→M→0, with G0, G1 is Gorenstein injective module.Gorenstein FP-projective modules were discussed in the end of the arti-cle, the equvelance of Gorenstein FP-projective mosules were also obtained.