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ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Completely lexsegment ideals


Authors: Emanuela De Negri and Jürgen Herzog
Journal: Proc. Amer. Math. Soc. 126 (1998), 3467-3473
MSC (1991): Primary 13C99, 13D02
MathSciNet review: 1452799
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Abstract: In this paper we study ideals which are generated by lexsegments of monomials. In contrast to initial lexsegments, the shadow of an arbitrary lexsegment is in general not again a lexsegment. An ideal generated by a lexsegment is called completely lexsegment, if all iterated shadows of the set of generators are lexsegments. We characterize all completely lexsegment ideals and describe cases in which they have a linear resolution. We also prove a persistence theorem which states that all iterated shadows of a lexsegment are again lexsegments if the first shadow has this property.


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Additional Information

Emanuela De Negri
Affiliation: FB 6 Mathematik und Informatik, Universität-GHS-Essen, Postfach 103764, Essen 45117, Germany
Email: mat304@uni-essen.de

Jürgen Herzog
Affiliation: FB 6 Mathematik und Informatik, Universität-GHS-Essen, Postfach 103764, Essen 45117, Germany
Email: mat300@uni-essen.de

DOI: https://doi.org/10.1090/S0002-9939-98-04379-2
Received by editor(s): February 7, 1997
Received by editor(s) in revised form: March 5, 1997
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1998 American Mathematical Society