Geodesic
On duality in the homology algebra of a Koszul complex
Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 77-81 Cet article a éte moissonné depuis la source Math-Net.Ru

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The homology algebra of the Koszul complex $K(x_1,\ldots,x_n;R)$ of a Gorenstein local ring $R$ has Poincaré duality if the ideal $I=(x_1,\ldots,x_n)$ of $R$ is strongly Cohen–Macaulay (i.e., all homology modules of the Koszul complex are Cohen–Macaulay) and under the assumption that $\dim R-\operatorname{grade}I\leq4$ the converse is also true. 
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E. S. Golod. On duality in the homology algebra of a Koszul complex. Fundamentalʹnaâ i prikladnaâ matematika, Tome 9 (2003) no. 1, pp. 77-81. http://geodesic.mathdoc.fr/item/FPM_2003_9_1_a6/

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