On the associated prime ideals of local cohomology modules defined by a pair of ideals

2015/02/17 by Amoli, Kh. Ahmadi, Habibi, Z., Jahangiri, M.
#13D45 #13E05 #13E10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.04978

Abstract

Let I and J be two ideals of a commutative Noetherian ring R and M be an R-module. For a non-negative integer n it is shown that, if the sets \Ass_R(\Extⁿ _R(R/I,M)) and \Supp_R(\Extⁱ_R(R/I,H^j_I,J (M))) are finite for all i ≤ n+1 and all j< n, then so is \linebreak\Ass_R(\Hom_R(R/I,Hⁿ_I,J(M))). We also study the finiteness of \Ass_R(\Extⁱ_R(R/I,Hⁿ_I,J (M))) for i=1,2.

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