7 problems

Salce–Zanardo conjecture. If $R$ satisfies $\operatorname{ID}_2$, then $R$ must be a Bézout domain.

Let $D$ be an integral domain. The constructible topology on the space of ideals is denoted by $\mathcal{I}(D)^{\mathrm{cons}}$, and $\mathrm{Princ}(D)$ denotes the set of principa…

Let $R$ be a commutative domain. Say that $R$ satisfies property $\operatorname{ID2}$ if every singular $2\times 2$ matrix over $R$ is a product of idempotent matrices. Idempotent-…

Let $R$ be a Bézout domain and let $W$ be a critically-finite element. Denote by $\mathbf{hef}(R,W)$ the subcategory of $\mathrm{hmf}(R,W)$ additively generated by elementary facto…

Let $R$ be a Bézout domain and let $W$ be a critically-finite element of $R$. Krull–Schmidt conjecture. The category $\mathrm{hmf}(R,W)$ is a Krull–Schmidt category. The claim foll…

Elementary-factorization generation conjecture. The inclusion functor $\iota$ is an equivalence of $R$-linear categories. This is established in the paper when $R$ is an elementary…

Let $R$ be a Bézout domain with prime elements, and let $W=W_0W_c$, where $W_0\in R^\times$ is square-free and $W_c\in R^\times$ is a finite product of primes with order at least t…