Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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


Author: David E. Rush
Journal: Proc. Amer. Math. Soc. 128 (2000), 2879-2884
MSC (1991): Primary 13A15, 13B25, 13B02
Published electronically: April 7, 2000
MathSciNet review: 1670427
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

Let $R$ be a commutative ring, let $X$be an indeterminate, and let $g \in R[X]$. There has been much recent work concerned with determining the Dedekind-Mertens number $\mu_R(g)$=min $\{ k \in \mathbb{N}\; \vert \; c_R(f)^{k-1} c_R(fg) = c_R(f)^{k} c_R(g) \mbox{ for all } f \in R[X] \}$, especially on determining when $\mu_R(g)$ = $1$. In this note we introduce a universal Dedekind-Mertens number $u \mu_R(g)$, which takes into account the fact that $\mu_S(g)$ $\leq$ deg($g$) + $1$ for any ring $S$ containing $R$ as a subring, and show that $u \mu_R(g)$behaves more predictably than $\mu_R(g)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13A15, 13B25, 13B02

Retrieve articles in all journals with MSC (1991): 13A15, 13B25, 13B02


Additional Information

David E. Rush
Affiliation: Department of Mathematics, University of California, Riverside, California 92507
Email: rush@math.ucr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05394-6
PII: S 0002-9939(00)05394-6
Keywords: Dedekind-Mertens lemma, Dedekind-Mertens number, content of a polynomial
Received by editor(s): September 16, 1998
Received by editor(s) in revised form: November 29, 1998
Published electronically: April 7, 2000
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society