Gorenstein Syzygy Modules

2009/03/26 by Huang, Chonghui, Huang, Zhaoyong · 1 citation
#16E05 #16E10 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0903.4514

Abstract

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 M∈ \mod R^op is a Gorenstein transpose of a module A∈ \mod R 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.

Cited by

• Base change of (Gorenstein) transpose, k-torsionfree modules, and quasi-faithfully flat extensions

Related

• Syzygy modules for quasi k-Gorenstein rings
• (n,m)-Strongly Gorenstein Projective Modules
• Syzygy Modules and Injective Cogenerators for Noether Rings
• Base change of (Gorenstein) transpose, k-torsionfree modules, and quasi-faithfully flat extensions
• Gorenstein dimension of modules