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On Duality in the Homology Algebra of a Koszul Complex

Research paper by E. S. Golod

Indexed on: 01 Aug '05Published on: 01 Aug '05Published in: Journal of Mathematical Sciences



Abstract

The homology algebra of the Koszul complex K(x1, ..., xn; R) of a Gorenstein local ring R has Poincare duality if the ideal I = (x1, ..., xn) 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.