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- W4387323851 abstract "Let $R$ be a commutative Noetherian ring, and let $mathfrak a$ be a proper ideal of $R$. Let $M$ be a non-zero finitely generated $R$-module with the finite projective dimension $p$. Also, let $N$ be a non-zero finitely generated $R$-module with $Nneqmathfrak{a} N$, and assume that $c$ is the greatest non-negative integer with the property that $operatorname{H}^i_{mathfrak a}(N)$, the $i$-th local cohomology module of $N$ with respect to $mathfrak a$, is non-zero. It is known that $operatorname{H}^i_{mathfrak a}(M, N)$, the $i$-th generalized local cohomology module of $M$ and $N$ with respect to $mathfrak a$, is zero for all $i>p+c$. In this paper, we obtain the coassociated prime ideals of $operatorname{H}^{p+c}_{mathfrak a}(M, N)$. Using this, in the case when $R$ is a local ring and $c$ is equal to the dimension of $N$, we give a necessary and sufficient condition for the vanishing of $operatorname{H}^{p+c}_{mathfrak a}(M, N)$ which extends the Lichtenbaum-Hartshorne vanishing theorem for generalized local cohomology modules." @default.
- W4387323851 created "2023-10-04" @default.
- W4387323851 creator A5071870290 @default.
- W4387323851 date "2023-10-01" @default.
- W4387323851 modified "2023-10-14" @default.
- W4387323851 title "Lichtenbaum-Hartshorne vanishing theorem for generalized local cohomology modules" @default.
- W4387323851 doi "https://doi.org/10.22055/jamm.2023.43821.2166" @default.
- W4387323851 hasPublicationYear "2023" @default.
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