Some applications of Cohen-Macaulay injective dimension

Year 2014, Volume: 43 Issue: 5, 777 - 785, 01.10.2014

Xi Tang

Abstract

Let a be an ideal of a commutative Noetherian ring R, M a finitely
generated R-module with finite projective dimension and N an arbitrary R-module with finite Cohen-Macaulay injective dimension. In
this paper, we show that the generalized local cohomology Hi
a(M, N)
is zero for every i larger than the Cohen-Macaulay injective dimension
of N. As applications, we obtain new characterizations of Gorenstein
and regular local rings. 

Keywords

Cohen-Macaulay injective dimension, dualizing module, generalized local cohomology, semidualizing module

References

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