4 problems

Multivariable Gaussian content conjecture. The one-variable theorem on Gaussian polynomials can be generalized to any number of indeterminates over any reduced ring; it is enough t…

Locally principal content conjecture. The polynomial $f$ is Gaussian if and only if its content $\mathfrak c(f)$ is locally principal.

Invertible-content conjecture. The content $\mathfrak c(f)$ is an invertible ideal of $R$.

Let $R$ be a commutative ring, and let $f\in R[x]$ be a Gaussian polynomial, meaning that $c(f)c(g)=c(fg)$ for every $g\in R[x]$, where $c(f)$ denotes the ideal generated by the co…