Article
A Note on Symmetry in the Vanishing of Ext
Rocky Mountain Journal of Mathematics
(2013)
Abstract
In [1] Avramov and Buchweitz proved that for finitely generated modules M and N over a complete intersection local ring R, ExtiR(M,N)=0 for all i>>0 implies ExtiR(N, M)=0 for all i>>0. In this note we give some generalizations of this result. Indeed we prove the above mentioned result when (1) M is finitely generated and N is arbitrary, (2) M is arbitrary and N has finite length and (3) M is complete and N is finitely generated.
Keywords
- Complete intersection ring,
- Complete module,
- Gorenstein ring
Disciplines
Publication Date
2013
DOI
10.1216/RMJ-2013-43-1-329
Publisher Statement
This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, the authors must hold the rights or the work must be under Creative Commons Attribution License, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Rocky Mountain Journal of Mathematics.
Citation Information
Saeed Nasseh and Massoud Tousi. "A Note on Symmetry in the Vanishing of Ext" Rocky Mountain Journal of Mathematics 43.1 (2013): 329-341.source:http://arxiv.org/abs/0904.4858
doi:10.1216/RMJ-2013-43-1-329
Available at: http://works.bepress.com/saeed_nasseh/3