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The Dedekind-Mertens lemma and the contents of polynomials
Author(s):
William
Heinzer;
Craig
Huneke
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1305-1309.
MSC (1991):
Primary 13A15, 13B25, 13G05, 13H10
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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  the integer  in the Dedekind-Mertens Lemma may be replaced by the number of local generators of the content of  . We also raise a question concerning the converse.
References:
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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