The content of a Gaussian polynomial is invertible

K. Alan Loper; Moshe Roitman

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arXiv · math/0309195

The content of a Gaussian polynomial is invertible

K. Alan Loper·Moshe Roitman

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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.

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BibTeX RIS

K. Alan Loper, Moshe Roitman. 2003-09-11. The content of a Gaussian polynomial is invertible. https://arxiv.org/abs/math/0309195

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