Geodesic
On a~homological characterization of a~certain class of local rings
Sbornik. Mathematics, Tome 38 (1981) no. 3, pp. 421-425

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It is shown that the nondegeneracy of the Yoneda product $\operatorname{Ext}_A^p(k,M)\times\operatorname{Ext}_A^{n-p}(M,k)$ ($M$ is either a noetherian module or a complex of finite projective dimension, and $k$ is the residue field) characterizes the regularity of the ring $A$, whereas the isomorphism $\operatorname{Ext}_A^p(k,M)\approx\operatorname{Ext}_A^{n-p} (M,k)$ characterizes the fact that $A$ is Gorenstein. Bibliography: 8 titles. 
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     author = {A. F. Ivanov},
     title = {On a~homological characterization of a~certain class of local rings},
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A. F. Ivanov. On a~homological characterization of a~certain class of local rings. Sbornik. Mathematics, Tome 38 (1981) no. 3, pp. 421-425. http://geodesic.mathdoc.fr/item/SM_1981_38_3_a6/