3 problems

Bazzoni–Glaz conjecture. The weak global dimension of a Gaussian ring is $0$, $1$, or $\infty$.

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…

Pseudo-arithmetical characterization conjecture. $R$ is pseudo-arithmetical if and only if the zero ideal is locally irreducible.