Kyungpook Mathematical Journal

  • 제58권1호
  • /
  • Pages.9-17
  • /
  • 2018
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

Results of Graded Local Cohomology Modules with respect to a Pair of Ideals

  • 투고 : 2017.06.28
  • 심사 : 2017.09.09
  • 발행 : 2018.03.23
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Let $R ={\oplus}_{n{\in}Z}R_n$ be a graded commutative Noetherian ring and let I be a graded ideal of R and J be an arbitrary ideal. It is shown that the i-th generalized local cohomology module of graded module M with respect to the (I, J), is graded. Also, the asymptotic behaviour of the homogeneous components of $H^i_{I,J}(M)$ is investigated for some i's with a specified property.

키워드

참고문헌

  1. M. P. Brodmann, R. Y. Sharp, Local cohomology: an algebraic introduction with geometric applications, Cambridge Univ. Press, Cambridge, 1998.
  2. W. Bruns, J. Herzog, Cohen-Macaulay ring, Cambridge Univ. Press, Cambridge, 1998.
  3. M. Jahangiri and Z. Habibi, On graded local cohomology modules defined by a pair of ideals, J. Agebr. Syst., 3(2)(2016), 133-146.
  4. K. Khashyarmanesh, Associated primes of graded components of generalized local co-homology modules, Comm. Algebra, 33(2005), 3081-3090. https://doi.org/10.1081/AGB-200066119
  5. P. H. Lima and V. H. Perez, Graded verson of local cohomology with respect to a pair of ideals, J. Commut. Algebra, 9(2017), 545-561. https://doi.org/10.1216/JCA-2017-9-4-545
  6. 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
  7. J. Rotman, An Introduction to homological algebra, Academic Press, Orlando, 1979.
  8. C.Rotthaus, L. M. Sega, Some properties of graded local cohomology modules, J. Algebra, 283(2005), 232-247. https://doi.org/10.1016/j.jalgebra.2004.07.034
  9. R. Takahashi, Y. Yoshino and T. Yoshinawa, Local cohomology based on a nonclosed support defined by a pair of ideals, J. Pure Appl. Algebra, 213(2009), 582-600. https://doi.org/10.1016/j.jpaa.2008.09.008
  10. N. Zamani, On the homogeneous pieces of graded generalized local cohomology modules, Colloq. Math., 97(2)(2003), 181-188. https://doi.org/10.4064/cm97-2-5