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) ∈ 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 language | English |
|---|---|
| Pages (from-to) | 1267-1271 |
| Number of pages | 5 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 133 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 2005 |
Keywords
- Content
- Gaussian polynomial
- Invertible ideal
- Locally principal
- Prestable ideal
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics