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- Title
Indecomposability of top local cohomology modules and connectedness of the prime divisors graphs.
- Authors
Doustimehr, Mohammad Reza
- Abstract
Let be an ideal of a Noetherian local ring R with dim R = d and t be a positive integer. In this paper, it is shown that the top local cohomology module H d (R) (equivalently, its Matlis dual H d (R) ∨ ) can be written as a direct sum of t indecomposable summands if and only if the endomorphism ring Hom R (H d (R) ∨ , H d (R) ∨) can be written as a direct product of t local endomorphism rings if and only if the set of minimal primes of R with H d (R /) ≠ 0 can be written as disjoint union of t non-empty subsets U 1 , U 2 , ... , U t such that for all distinct i , j ∈ { 1 , ... , t } and all ∈ U i and all ∈ U j , we have ht (+) ≥ 2. This generalizes Theorem 3.6 of Hochster and Huneke [Contemp. Math. 159 (1994) 197–208].
- Subjects
INDECOMPOSABLE modules; ENDOMORPHISM rings; LOCAL rings (Algebra); NOETHERIAN rings
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 8, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S021949882350161X