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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A generalized Dedekind-Mertens lemma and
its converse


Authors: Alberto Corso, William Heinzer and Craig Huneke
Journal: Trans. Amer. Math. Soc. 350 (1998), 5095-5109
MSC (1991): Primary 13A15; Secondary 13B25, 13G05, 13H10
MathSciNet review: 1473435
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Abstract: We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind-Mertens and prove the converse under suitable dimensionality restrictions.


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Additional Information

Alberto Corso
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
Address at time of publication: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: corso@math.msu.edu

William Heinzer
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
Email: heinzer@math.purdue.edu

Craig Huneke
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47906
Email: huneke@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02176-X
PII: S 0002-9947(98)02176-X
Keywords: Content ideal of a polynomial, integral closure of an ideal, Dedekind--Mertens Lemma, Dedekind--Mertens number
Received by editor(s): February 10, 1997
Additional Notes: The authors gratefully acknowledge partial support from the NSF
Dedicated: To Wolmer V. Vasconcelos on the occasion of his sixtieth birthday
Article copyright: © Copyright 1998 American Mathematical Society