Gorenstein同调代数是经典的同调代数的推广。 Gorenstein 模与Gorenstein 同调维数是Gorenstein 同调代数的主要研究对象，而Banach代数是泛函分析中的重要研究方向。Liddell等人用同调的方法去研究Banach 代数的结构与性质，从而把经典的同调代数与Banach 代数结合起来。本项目旨在把Gorenstein同调代数的部分理论引入Banach代数并用Gorenstein同调的方法去刻画Banach代数，从而把两个不同的方向联系起来，并以此来验证H.Holm的关于同调模类的猜想。

The Gorenstein homological algebra was the promotion of classical homological algebra. The Gorenstein modules and the Gorenstein homological dimensions were the main objects of the Gorenstein homological algebra, the Banach algebra was an important component of functional analysis. Liddell et al. used the homology methods to study the structure and properties of the Banach algebra, and then they combined the classical homological algebra and Banach algebra. Our project aims to introduce the Gorenstein homological theories to the Banach algebra, and use the methods of Gorenstein homological theories to characterize the Banach algebra. It combines two different directions and then verifies the conjecture of Gorenstein modules of H.Holm.