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Some Properties of Serre Subcategories in the Graded Local Cohomology Modules

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  • Feysal Hassani
  • Rasul Rasuli

Abstract

Let be a standard homogeneous Noetherian ring with local base ring and let be a finitely generated graded -module. Let be the th local cohomology module of with respect to . Let be a Serre subcategory of the category of -modules and let be a nonnegative integer. In this paper, if then we investigate some conditions under which the -modules and are in for all . Also, we prove that if , then the graded -module is in for all . Finally, we prove that if is the biggest integer such that , then for all .

Suggested Citation

  • Feysal Hassani & Rasul Rasuli, 2017. "Some Properties of Serre Subcategories in the Graded Local Cohomology Modules," Journal of Mathematics, Hindawi, vol. 2017, pages 1-6, July.
    • Handle: RePEc:hin:jjmath:5230589
    DOI: 10.1155/2017/5230589
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