Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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INJECTIVE DIMENSIONS OF LOCAL COHOMOLOGY MODULES

  • Received : 2016.07.09
  • Accepted : 2016.12.15
  • Published : 2017.07.31
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Abstract

Assume that R is a commutative Noetherian ring with non-zero identity, a is an ideal of R, X is an R-module, and t is a non-negative integer. In this paper, we present upper bounds for the injective dimension of X in terms of the injective dimensions of its local cohomology modules and an upper bound for the injective dimension of $H^t_{\alpha}(X)$ in terms of the injective dimensions of the modules $H^i_{\alpha}(X)$, $i{\neq}t$, and that of X. As a consequence, we observe that R is Gorenstein whenever $H^t_{\alpha}(R)$ is of finite injective dimension for all i.

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References

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