Homological Properties Of F-Gorenstein Modules And Complexes

Let ? be an Artin algebra over a commutative Artin ring k, F an additive subb-ifunctor of the additive bifunctor Ext_?~1(-,-) and have enough projectives and injec-tivcs. In this paper, we study the stability of F-Gorcnstcin projectivc modules and F-Gorenstein projective complexes. Firstly, we show the stability of F-Gorenstein pro-ject ive modules. Secondly, we get the stability of F-Gorenstein projective complexes by discussing the structure of F-Gorenstein projective complexes. Finally, we con-sider the Tate cohomology of modules in view of F-Gorenstein projective modules and obtaine the balance property and the Avramov-Martsinkovsky sequence about classical, relative and Tate cohomology.