Gorenstein homological dimensions
Gorenstein homological dimensions
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DOI：
10.1016/j.jpaa.2003.11.007
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发表时间：
2004-05
影响因子：
0.8
通讯作者：
Henrik Holm
中科院分区：
文献类型：
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作者：
Henrik Holm
在基本同调代数中，模的投射维数、内射维数和平坦维数起着重要的基础作用。本文研究了与之密切相关的Gorenstein投射维数、Gorenstein内射维数和Gorenstein平坦维数。关于特殊交换Noether环上的Gorenstein维数有很多好的结果，通常是具有对偶模的局部Cohen-Macaulay环。这些结果是由Avramov，Christensen，Enochs，Foxby，Jenda，Martsinkovsky和Xu等人完成的。本文的目的是推广这些结果，并给出任意结合环上Gorenstein维数的同调描述。
In basic homological algebra, the projective, injective and flat dimensions of modules play an important and fundamental role. In this paper, the closely related Gorenstein projective, Gorenstein injective and Gorenstein flat dimensions are studied. There is a variety of nice results about Gorenstein dimensions over special commutative noetherian rings; very often local Cohen–Macaulay rings with a dualizing module. These results are done by Avramov, Christensen, Enochs, Foxby, Jenda, Martsinkovsky and Xu among others. The aim of this paper is to generalize these results, and to give homological descriptions of the Gorenstein dimensions over arbitrary associative rings.