Gorenstein dimension and AS—Gorenstein algebras
Gorenstein dimension and AS—Gorenstein algebras
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Gorenstein 维数和 AS—Gorenstein 代数
DOI：
10.1080/00927872.2013.807111
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发表时间：
2014
影响因子：
0.7
通讯作者：
Kenta Ueyama
中科院分区：
文献类型：
--
作者：
Kazunori Minetaki;Yuji Akematsu;Masatsugu Tsuji;長谷川祐;明松祐司;Kenta Ueyama
本文的目的是将Gorenstein维的概念与AS-Gorenstein代数联系起来。特别地，我们证明了具有平衡对偶化复形的Notherian连通分次代数是AS-Gorenstein的，如果平衡对偶化复形具有有限的Gorenstein维。作为准备，我们将Auslander-Bridger公式推广到一类具有平衡对偶复形的非交换Noether连通分次代数。
The purpose of this paper is to connect the notion of Gorenstein dimension with AS-Gorenstein algebras. In particular, we show that a noetherian connected graded algebra having a balanced dualizing complex is AS-Gorenstein if the balanced dualizing complex has finite Gorenstein dimension. As a preparation, we generalize the Auslander–Bridger formula to the class of noncommutative noetherian connected graded algebras having balanced dualizing complexes.