FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 1, PAGES 77-81

On duality in the homology algebra of a Koszul complex

E. S. Golod

Abstract

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The homology algebra of the Koszul complex $K(x$₁, ¼,x_n;R) of a Gorenstein local ring $R$ has Poincaré duality if the ideal $I\; =\; (x$₁, ¼,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 $dim\; R$- grade I £ 4 the converse is also true.

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Last modified: April 4, 2004.