Geodesic
On Cohen-Macaulay rings
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 2, pp. 223-230.

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In this paper, we use a characterization of $R$-modules $N$ such that $fd_RN = pd_RN$ to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting $N$ to be the $dth$ local cohomology functor of $R$ with respect to the maximal ideal where $d$ is the Krull dimension of $R$.
Classification : 13C14, 13D02, 13D05, 13D45, 13H10, 18G10, 18G20
Keywords: injective; precovers; preenvelopes; canonical module; Cohen-Macaulay; \newline $n$-Gorenstein; resolvent; resolutions 
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     author = {Enochs, Edgar E. and Overtoun, Jenda M. G.},
     title = {On {Cohen-Macaulay} rings},
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Enochs, Edgar E.; Overtoun, Jenda M. G. On Cohen-Macaulay rings. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 2, pp. 223-230. http://geodesic.mathdoc.fr/item/CMUC_1994__35_2_a1/