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RESULTS OF CERTAIN LOCAL COHOMOLOGY MODULES

  • Mafi, Amir (University of Kurdistan Pasdaran ST.) ;
  • Talemi, Atiyeh Pour Eshmanan (Atiyeh Pour Eshmanan Talemi Islamic Azad University Science and Research Branch)
  • Received : 2012.05.30
  • Published : 2014.05.31

Abstract

Let R be a commutative Noetherian ring, I and J two ideals of R, and M a finitely generated R-module. We prove that $$Ext^i{_R}(R/I,H^t{_{I,J}}(M))$$ is finitely generated for i = 0, 1 where t=inf{$i{\in}\mathbb{N}_0:H^2{_{I,J}}(M)$ is not finitely generated}. Also, we prove that $H^i{_{I+J}}(H^t{_{I,J}}(M))$ is Artinian when dim(R/I + J) = 0 and i = 0, 1.

Keywords

local cohomology;Artinian modules

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