Abstract
The homology algebra of the Koszul complex K(x 1, ..., x n ; R) of a Gorenstein local ring R has Poincare duality if the ideal I = (x 1, ..., 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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REFERENCES
L. L. Avramov and E. S. Golod, “On the homology algebra of the Koszul complex of a local Gorenstein ring, ” Mat. Zametki, 9, No.1, 53–58 (1971).
M. Auslander and M. Bridger, Stable Module Theory, Mem. Amer. Math. Soc., vol. 94 (1969).
J. Tate, “Homology of Noetherian rings and local rings,” Illinois J. Math., 1, no.1, 14–27 (1957).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 77–81, 2003.
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Golod, E.S. On Duality in the Homology Algebra of a Koszul Complex. J Math Sci 128, 3381–3383 (2005). https://doi.org/10.1007/s10958-005-0276-y
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DOI: https://doi.org/10.1007/s10958-005-0276-y