Abstract
It is proved that local Gorenstein rings have the property that the homology algebra of their Koszul complex is a Poincaré algebra.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
J.-P. Serre, “Local algebra and the theory of conciseness,” Matematika,7, No. 5, 3–93 (1963).
E. F. Assmus, “On the homology of local rings,” Illinois J. Math.,13, No. 2, 187–199 (1959).
M. Auslander and D. A. Buchsbaum, “Codimension and multiplicity,” Ann. Math.,68, 625–657 (1958).
H. Bass, “On the ubiquity of Gorenstein rings,” Math. Z.,82, No. 1, 2–28 (1963).
M. P. Murthy, “A note on the ‘Primbasissatz,’ ” Arch. Math.,12, No. 4, 425–428 (1961).
J.-P. Serre, Sur la Dimension Homologique des Anneaux et des Modules Noetheriens, Proc. Internat. Sympos. Algebr. Number Theory, 1955, Tokyo (1956), pp. 175–189.
J. Tate, “Homology of noetherian rings and local rings,” Illinois J. Math.,1, No. 1, 14–27 (1957).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 9, No. 1, pp. 53–58, January, 1971.
Rights and permissions
About this article
Cite this article
Avramov, L.L., Golod, E.S. Homology algebra of the Koszul complex of a local Gorenstein ring. Mathematical Notes of the Academy of Sciences of the USSR 9, 30–32 (1971). https://doi.org/10.1007/BF01405047
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01405047