9 problems

Hereditary atomicity conjecture. Every hereditarily atomic domain satisfies the ACCP.

Let $R$ be a domain. It is pseudo-integrally closed when $R=\widetilde{R}=\bigcup(I_t:I_t)$, where $I$ ranges over the finitely generated ideals of $R$. A Krull-type domain is a Pr…

Let $D$ be an integral domain, and let $R(D)$ denote its reciprocal complement, the subring generated by the inverses of all nonzero elements of $D$. Dimension conjecture. For any…

Let an hereditarily atomic integral domain be an integral domain whose every subring is atomic, and let ACCP denote the ascending chain condition on principal ideals. The ACCP conj…

Krull-dimension conjecture. The inequality

Let Figure $1$ be the directed diagram of implications among unique factorization domains, atomic domains, semi-atomic domains, almost atomic domains, quasi-atomic domains, Fursten…

Let the classes of rings in Figure $1$ be the unique factorization domains, atomic domains, semi-atomic domains, almost atomic domains, quasi-atomic domains, Furstenberg domains, s…

Let $A$ be an integral domain. An H-domain is a domain in which $t$-maximal ideals are divisorial. Glaz–Vasconcelos conjecture. In an H-domain, faithfully flat ideals should be pro…

Cameron's conjecture. $G$ is entire, respectively strongly entire, if and only if it has no finite orbit on $E$.