The content of a Gaussian polynomial is invertible
Commutative Algebra
2007-05-23 v1
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 c(f) generated by the coefficients of f. The polynomial f(X) is called Gaussian if c(fg)=c(f)c(g) for all g(X) in R[X]. It is well known that if c(f) is an invertible ideal, then f is Gaussian. In this note we prove the converse.
Keywords
Cite
@article{arxiv.math/0309195,
title = {The content of a Gaussian polynomial is invertible},
author = {K. Alan Loper and Moshe Roitman},
journal= {arXiv preprint arXiv:math/0309195},
year = {2007}
}
Comments
6 pages