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.

Location: http://mech.math.msu.su/~fpm/eng/k03/k031/k03107h.htm

Last modified: April 4, 2004.