Behavior of the Auslander condition with respect to regradings
Behavior of the Auslander condition with respect to regradings
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DOI：
10.1142/s0219498819501688
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发表时间：
2017-04
影响因子：
0.8
通讯作者：
G.-S. Zhou;Y. Shen;D. Lu
中科院分区：
文献类型：
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作者：
G.-S. Zhou;Y. Shen;D. Lu
证明了由有限阶交换群分次的Notherian环当且仅当它满足分次Auslander条件。此外，我们还从与Auslander条件相同的角度研究了内射维度、整体维度和Cohen-Macaulay性质。我们方法的一个关键步骤是建立分次环[公式：见文本]、它的模为理想的商环[公式：见文本]和它的局部化环关于Ore集[公式：见文本]之间的同调关系，其中[公式：见文本]是[公式：见文本]的齐次正则正规不可逆元。
We show that a noetherian ring graded by an abelian group of finite rank satisfies the Auslander condition if and only if it satisfies the graded Auslander condition. In addition, we also study the injective dimension, the global dimension and the Cohen–Macaulay property from the same perspective as that for the Auslander condition. A key step of our approach is to establish homological relations between a graded ring [Formula: see text], its quotient ring modulo the ideal [Formula: see text] and its localization ring with respect to the Ore set [Formula: see text], where [Formula: see text] is a homogeneous regular normal non-invertible element of [Formula: see text].