Abstract
Let \({(R, \mathfrak{m})}\) be a commutative Noetherian local ring of Krull dimension d, and let C be a semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing module if and only if the top local cohomology module of \({R, H _{\mathfrak{m}} ^{d} (R)}\), has finite G C -injective dimension. This generalizes a recent result due to Yoshizawa, where the ring is assumed to be complete Cohen-Macaulay.
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The research of S. Yassemi was in part supported by a grant from IPM No. 91130214.
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Salimi, M., Tavasoli, E. & Yassemi, S. Top local cohomology modules and Gorenstein injectivity with respect to a semidualizing module. Arch. Math. 98, 299–305 (2012). https://doi.org/10.1007/s00013-012-0371-5
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DOI: https://doi.org/10.1007/s00013-012-0371-5