DOI QR코드

DOI QR Code

MINIMAXNESS OF LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS

Abbasi, A.;Roshan Shekalgourabi, H.

  • Received : 2011.10.26
  • Accepted : 2011.12.06
  • Published : 2012.06.25

Abstract

Let R be a commutative Noetherian ring and I, J be ideals of R. We introduced the notion of (I; J)-cominimax R-modules. For an integer $n$ and an R-module M, let $H^i_{I,J}(M)$ be an (I; J)-cominimax R-module for all $i<n$. The J-minimaxness of some Ext modules of $H^n_{I,J}(M)$ is investigated. Among of the obtaining results, there is a generalization of the main result of [1].

Keywords

Local cohomology modules;J-minimax modules;(I, J)-cominimax modules

References

  1. J. Azami, R. Naghipour, and B. Vakili, Finiteness properties of local cohomology modules for a-minimax modules, Proc. Amer. Math. Soc. 137 (2009), no. 2, 439-448.
  2. M. H. Bijan-Zadeh, A common generalization of local cohomology theories, Glasgow Math. J. 21 (1980), no. 2, 173-181. https://doi.org/10.1017/S0017089500004158
  3. K. Divaani-Aazar and M. Esmkhani, Artinianness of local cohomology modules of ZD-modules, Comm. Algebra 33 (2005), 2857-2863. https://doi.org/10.1081/AGB-200063983
  4. L. Melkersson, On asymptotic stability for sets of prime ideals connected with the powers of an ideal, Math. Proc. Cambridge Philos. Soc. 107 (1990), 267-271. https://doi.org/10.1017/S0305004100068535
  5. L. Melkersson, Modules cofinite with respect to an ideal, J. Algebra 285 (2005), 649-668. https://doi.org/10.1016/j.jalgebra.2004.08.037
  6. R. Takahashi, Y. Yoshino, and T. Yoshizawa, Local cohomology based on a non- closed support de ned by a pair of ideals, J. Pure Appl. Algebra 213 (2009), no. 4, 582-600. https://doi.org/10.1016/j.jpaa.2008.09.008
  7. A. Tehranian and A. Pour Eshmanan Talemi, Cofiniteness of local cohomology based on a nonclosed support de ned by a pair of ideals, Bull. Iranian. Math. Soc. 36 (2010), no. 2, 145-155.
  8. P. Vamos and D.W. Sharpe, Injective modules, Cambridge University Press, London-New York, 1972.
  9. W. Vasconcelos, Divisor theory in module categories, North-Holland Publishing Company, Amsterdam, 1974.
  10. H. Zoschinger, Minimax-moduln, J. Algebra 102 (1986), 1-32. https://doi.org/10.1016/0021-8693(86)90125-0