The content of a Gaussian polynomial IS invertible

K. Alan Loper, Moshe Roitman

Research output: Contribution to journalArticlepeer-review


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) ∈ 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.

Original languageEnglish
Pages (from-to)1267-1271
Number of pages5
JournalProceedings of the American Mathematical Society
Issue number5
StatePublished - May 2005


  • Content
  • Gaussian polynomial
  • Invertible ideal
  • Locally principal
  • Prestable ideal

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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