The content of a Gaussian polynomial is invertible

Details The content of a Gaussian polynomial is invertible The content of a Gaussian polynomial is invertible

2003-09-11

arxiv.org/abs/math/0309195v1

Mathematics

Commutative Algebra

6 pages

Scientific paper

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.

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