In this paper, we introduce a class of exact structures in terms of finiteness conditions of modules, which are called n-pure exact structures. We investigate the properties of n-pure derived categories of module categories using n-pure exact structures, and show that n-pure derived categories share many nice properties of classical derived categories. In particular, we show that bounded n-pure derived categories can be realized as certain homotopy categories. We also compare the classical bounded derived categories and the bounded n-pure derived categories, and show that the former can be described by n-pure projective modules.

中文翻译：

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有限条件和相对派生类别

在本文中，我们根据模块的有限性条件介绍了一类精确结构，称为n-纯精确结构。我们使用n-纯精确结构研究模块类别的n-纯派生类别的属性，并显示n-纯派生类别共享经典派生类别的许多好特性。特别地，我们表明有界的n-纯派生类别可以实现为某些同伦类别。我们还比较了经典有界派生类别和有界n-纯派生类别，并表明前者可以由n-纯射影模块描述。