A Gorenstein ring, $R$, is a commutative Noetherian local ring of finite injective dimension over itself. It follows then that its injective dimension is equal to $r$ = Krull dimension$(R)$, and that $Ext^{\ast}_R(k, R)$ is one dimensional as a $k$-vector space, where $k$ is the residue field of $R$.
Hyman Bass, 1963, On the ubiquity of Gorenstein rings, Mathematische Zeitschrift, 82: 8–28.
William Dwyer, John Greenlees, Srikanth Iyengar, Duality in algebra and topology, Advances in Maths
200 (2006) 357-402, (arXiv:math/0510247)
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