|
|||||
|
|
Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module |
|
| Authors: | Maryam Salimi Elham Tavasoli Siamak Yassemi |
| Institution: | 1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran 2. Department of Mathematics, University of Tehran, Tehran, Iran 3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran |
| Abstract: | Let ${(R, \mathfrak{m})}$ be a commutative Noetherian local ring of Krull dimension d, and let C be a semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing module if and only if the top local cohomology module of ${R, H _{\mathfrak{m}} ^{d} (R)}$ , has finite G C -injective dimension. This generalizes a recent result due to Yoshizawa, where the ring is assumed to be complete Cohen-Macaulay. |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |