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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Dedekind-Mertens lemma
and the contents of polynomials


Authors: William Heinzer and Craig Huneke
Journal: Proc. Amer. Math. Soc. 126 (1998), 1305-1309
MSC (1991): Primary 13A15, 13B25, 13G05, 13H10
MathSciNet review: 1425124
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a sharpening of the Dedekind-Mertens Lemma relating the contents of two polynomials to the content of their product. We show that for a polynomial $g$ the integer $1 + \deg (g)$ in the Dedekind-Mertens Lemma may be replaced by the number of local generators of the content of $g$. We also raise a question concerning the converse.


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Additional Information

William Heinzer
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395
Email: heinzer@math.purdue.edu

Craig Huneke
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395
Email: huneke@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04165-3
PII: S 0002-9939(98)04165-3
Keywords: Dedekind-Mertens Lemma, content of a polynomial
Received by editor(s): July 9, 1996
Received by editor(s) in revised form: October 23, 1996
Additional Notes: The second author was partially supported by the NSF
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1998 American Mathematical Society