Bass numbers of local cohomology modules with respect a pair of ideals

2013/06/12 by Sh. Payrovi, Payrovi, Sh., M. Lotfi Parsa +3
Mathematics · #13D07 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D07 #msc:13D45

paper · pdf · doi:10.48550/arxiv.1306.2779

8 pages

arxiv created 2013/07/01 · arxiv updated 2013/07/02

Abstract

Let R be a Noetherian local ring, I and J two ideals of R, M an R-module and s and t two integers. We study the relationship between the Bass numbers of M and Hⁱ_I,J(M). We show that μ^t(M)≤∑_i=0^tμ^t-i(Hⁱ_I,J(M)) and μ^s(H^t_I,J(M))≤ ∑_i=0^t-1μ^s+t+1-i(Hⁱ_I,J(M))+μ^s+t(M)+∑_i=t+1^s+t-1μ^s+t-1-i(Hⁱ_I,J(M)). As a consequence, it follows that if I is a principal ideal of R and M is a minimax R-module, then μ^j(Hⁱ_I,J(M)) is finite for all i∈\Bbb N₀ and all j∈\Bbb N₀.

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