Resolutions And Strongly ζ-gorenstein Projective Objects In A Triangulated Category

We introduce and study several main properties and generalizations of ζ-Gorenstein projective objects in a triangulated category.In the first part, we first define strongly ζ-exact complex and strongly ζ-projective resolution, we provide a method to construct a resolution of the first or third term in a triangle. Furthermore, we get the stability of ζ-Gorenstein projec-tive objects in a new method.In the second part, we study the typical properties of strongly ζ-Gorenstein projective objects based on the definition of the strongly ζ-Gorenstein projec-tive objects, we get that the class of ζ-Gorenstein objects is closed under exten-sion and the class of strongly ζ-Gorenstein projective objects is not closed un-der extension. Then we introduce the class between ζ-Gorenstein objects and strongly ζ-Gorenstein objects, which is called Ext-SGP(ζ), based on the relationsζ-projective objectsCstrongly ζ-Gorenstein projective objects(?)ζ-Gorenstein pro-jective objects and we give their properties.