The Dedekind-Mertens Lemma and the contents of polynomials

Heinzer, William; Huneke, Craig

doi:10.1090/S0002-9939-98-04165-3

The Dedekind-Mertens Lemma and the contents of polynomials
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by William Heinzer and Craig Huneke PDF

Proc. Amer. Math. Soc. 126 (1998), 1305-1309 Request permission

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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