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Gorenstein quotients by principal ideals offree Koszul homology

Published online by Cambridge University Press:  07 August 2001

JOSÉ J. M. SOTO
JOSÉ J. M. SOTO
Affiliation:
Departamento de Álgebra, Facultad de Matemáticas, Universidad de Santiago de Compostela, E-15771 Santiago de Compostela, Spain
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Abstract

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Let A be a noetherian local ring, x a non-unit element of A, B=A/(x). Let E be the Koszul complex associated to an arbitrary set of generators of the ideal (x) of A. Assume that H1(E) is a free B-module. Then A is Gorenstein if and only if B is also.

1991 Mathematics Subject Classification 13H10, 13D03.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 1 , March 2000 , pp. 51 - 54
Copyright
2000 Glasgow Mathematical Journal Trust