On the Vanishing Properties of Local Cohomology Modules Defined by a Pair of Ideals
Keywords:
Artinian module, Cofinite module, Local cohomology, Noetherian module.Abstract
As a generalization of the ordinary local cohomology modules, recently some authors introduced the local cohomology modules with respect to a pair of ideals. In this paper, we get some results on Artinianness, vanishing, finiteness and other properties of these modules. Let
Â
R be a commutative Noetherian ring, I , J two ideals of R and M a finitely generated R-module such that dimR M = n. We prove that Hn I ,J (M)/JHn I ,J (M) is I -cofinite Artinian and Hn I ,J (M)/IHn I ,J (M) has finite length. Also we show that, if R is local with dimR/I + J = 0 and dimR M/JM = d > 0, then Hd I ,J (M) is not finitely generated.
Downloads
Published
Issue
Section
License
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.