Gorenstein syzygy modules

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• 作者：Chonghui Huang ; Zhaoyong Huang
• 关键词：Gorenstein projective modules ; Gorenstein n-syzygy modules ; n-syzygy modules ; Gorenstein projective dimension ; Gorenstein transpose
• 刊名：Journal of Algebra
• 出版年：2010
• 出版时间：15 December 2010
• 年：2010
• 卷：324
• 期：12
• 页码：3408-3419
• 全文大小：155 K

文摘

For any ring R and any positive integer n, we prove that a left R-module is a Gorenstein n-syzygy if and only if it is an n-syzygy. Over a left and right Noetherian ring, we introduce the notion of the Gorenstein transpose of finitely generated modules. We prove that a module is a Gorenstein transpose of a module if and only if M can be embedded into a transpose of A with the cokernel Gorenstein projective. Some applications of this result are given.