In this paper, we first study the Gorenstein projective/flat dimension of complexes of modules. The relation between the Gorenstein projective/flat dimension for complexes and that for modules are investigated. Then we study Tate, stable and unbounded homology for complexes of modules. In the case of module arguments, we get some results that improve the known results.

中文翻译：

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络合物的同源理论和Gorenstein维数

在本文中，我们首先研究模块复合物的Gorenstein投影/平面维。研究了复合物的Gorenstein射影/平面尺寸与模块的尺寸之间的关系。然后，我们研究了模块复合物的Tate，稳定和无界同源性。对于模块参数，我们得到了一些改进已知结果的结果。