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Ideals with sliding depth

Published online by Cambridge University Press:  22 January 2016

J. Herzog ,
W.V. Vasconcelos  and
R. Villarreal
J. Herzog
Affiliation:
Fachbereich Mathematik, Universität Essen, D-4300 Essen 1, W. Germany
W.V. Vasconcelos
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, USA
R. Villarreal
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, USA
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We study here a class of ideals of a Cohen-Macaulay ring {R, m} somewhat intermediate between complete intersections and general Cohen-Macaulay ideals. Its definition, while a bit technical, rapidly leads to the development of its elementary properties. Let I = (x1 … xn) = (x) be an ideal of R and denote by H*(x) the homology of the ordinary Koszul complex K*(x) built on the sequence x. It often occurs that the depth of the module Hi i > 0, increases with i (as usual, we set depth (0) = ∞).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 99 , September 1985 , pp. 159 - 172
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

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