The content of a Gaussian polynomial is invertible
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- by K. Alan Loper and Moshe Roitman PDF
- Proc. Amer. Math. Soc. 133 (2005), 1267-1271 Request permission
Abstract:
Let $R$ be an integral domain and let $f(X)$ be a nonzero polynomial in $R[X]$. The content of $f$ is the ideal $\mathfrak c(f)$ generated by the coefficients of $f$. The polynomial $f(X)$ is called Gaussian if $\mathfrak c(fg) = \mathfrak c(f)\mathfrak c(g)$ for all $g(X) \in R[X]$. It is well known that if $\mathfrak c(f)$ is an invertible ideal, then $f$ is Gaussian. In this note we prove the converse.References
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Additional Information
- K. Alan Loper
- Affiliation: Department of Mathematics, Ohio State University-Newark, Newark, Ohio 43055
- Email: lopera@math.ohio-state.edu
- Moshe Roitman
- Affiliation: Department of Mathematics, University of Haifa, Haifa 31905, Israel
- Email: mroitman@math.haifa.ac.il
- Received by editor(s): September 16, 2003
- Published electronically: December 15, 2004
- Additional Notes: The second author thanks the Mathematics Department of Ohio State University for its hospitality
- Communicated by: Bernd Ulrich
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1267-1271
- MSC (2000): Primary 13B25
- DOI: https://doi.org/10.1090/S0002-9939-04-07826-8
- MathSciNet review: 2111931