中文摘要：

引入了三角范畴中一类特殊的对象,称其为（n,m）-强ξ-Gorenstein投射对象（简记为（n,m）-ξ-SG-投射对象）,其中n≥1且m≥0.主要研究这类对象的ξ-Gorenstein投射维数及其合冲,并且给出了任一对象的ξ-Gorenstein投射维数小于m的充要条件.

英文摘要：

A particular case of objects in triangulated categories are introduced, which are called （n, m）-strongly ξ-Gorenstein projective objects （（n, m）-ξ-SG-projective objects for short） （for integers n ≥ 1 and m ≥ 0）. The paper is mainly interested in studying the ξ-Gorenstein projective dimension and the syzygies of these objects. As consequences, the necessary and the sufficient conditions of an object are shown which has the ξ-Gorenstein projective dimension at most m.