Lower bounds for finiteness of generalized local cohomology modules and their associated primes

Details Lower bounds for finiteness of generalized local cohomology modules and their associated primes Lower bounds for finiteness of generalized local cohomology modules and their associated primes

2011-07-25

arxiv.org/abs/1107.5079v3

Mathematics

Commutative Algebra

10 pages, some changes has been done

Scientific paper

Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, $M$ a finite $R$--module and $X$ an arbitrary $R$--module. In this paper, we study relations between finiteness of local cohomology and generalized local cohomology modules in several cases. We characterize the membership of generalized local cohomology modules in a certain Serre class from lower bounds and we found the least integer such that these modules belong to that Serre class. Let $n$ be a non-negative integer, we prove that $\underset{i< n}\bigcup \Supp_R(\lc^{i}_{\fa}(M,X))= \underset{i< n}\bigcup \Supp_R(\lc^{i}_{\fa+\Ann_R{M}}(X)) = \underset{i< n}\bigcup \Supp_R(\Ext^{i}_{R}(M/{\fa}M,X))$ and if $\lc^{i}_{\fa}(M,X)=0$ for all $i

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