Proper Resolutions and Gorenstein Categories
Proper Resolutions and Gorenstein Categories
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DOI：
10.1016/j.jalgebra.2013.07.008
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发表时间：
2012-03
期刊：
影响因子：
--
通讯作者：
Zhaoyong Huang
中科院分区：
文献类型：
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作者：
Zhaoyong Huang
设A是阿贝尔范畴，C是A的加法满子范畴.我们提供了一种构造适当的C-归结的方法（分别为：余适当的C-共分解）的一项在一个短的正合序列A从其他两个条款。利用这些构造，我们肯定地回答了Sather-Wagstaff，Sharif和白色提出的Gorenstein范畴G（C）的稳定性问题，并证明了G（C）在直和项下是闭的.此外，我们还得到了计算A中对象的C-维数和G（C）-维数的一些准则。
Let A be an abelian category and C an additive full subcategory of A. We provide a method to construct a proper C-resolution (resp. coproper C-coresolution) of one term in a short exact sequence in A from that of the other two terms. By using these constructions, we answer affirmatively an open question on the stability of the Gorenstein category G (C) posed by Sather-Wagstaff, Sharif and White; and also prove that G (C) is closed under direct summands. In addition, we obtain some criteria for computing the C-dimension and the G (C)-dimension of an object in A.