Bass numbers of generalized local cohomology modules | Zendy

Sh. Payrovi | Zendy; S. Babaei | Zendy; I. Khalili-Gorji | Zendy

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Bass numbers of generalized local cohomology modules

Author(s) -

Sh. Payrovi,

S. Babaei,

I. Khalili-Gorji

Publication year - 2015

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim140620001p

Subject(s) - local cohomology , mathematics , noetherian ring , cohomology , bass (fish) , bounded function , corollary , pure mathematics , finitely generated abelian group , combinatorics , discrete mathematics , mathematical analysis , ecology , biology

Let R be a Noetherian ring, M a finitely generated R-module and N an arbitrary R-module. We consider the generalized local cohomology modules, with respect to an arbitrary ideal I of R, and prove that, for all nonnegative integers r, t and all p Spec(R) the Bass number μr(p,HtI (M,N)) is bounded above by Σtj=0μr(p, t−jExtR (M,HjI (N))). A corollary is that Ass (HtI (M,N) Utj=0 Ass (t−jExtR (M,HjI(N))). In a slightly different direction, we also present some well known results about generalized local cohomology modules.

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