Sally’s open problem on uniform bounds for generators versus dimension

Determine whether the existence of a uniform bound on the minimal number of generators of all prime ideals in a ring implies that the ring has Krull dimension at most two.

Background

The authors connect their construction of prime ideals with arbitrarily large minimal numbers of generators to broader structural questions about rings, highlighting Sally’s problem concerning whether such uniform bounds force low dimension.

They indicate that progress on constructing and understanding these prime ideals may contribute to resolving the dimensional consequence posed by Sally.

References

In the same vein, it may help to face the open problem stated by Sally in [19, Remark p. 53] on whether a uniform bound on the number of generators of prime ideals implies that the ring has dimension at most two.

— Explicit minimal generating sets of a family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring  (2604.00638 - González et al., 1 Apr 2026) in Section 1. Introduction