Stable-rank bound for special biserial algebras with a band

Let $\Lambda$ be a special biserial algebra with at least one band, and let $\mathrm{st}(\Lambda)$ denote its stable rank. Stable-rank conjecture. The stable rank satisfies

$$\omega\leq\mathrm{st}(\Lambda)<\omega^2.$$

This is proposed as a desirable generalization of a known result for the setting considered in the paper. Its status is not established in the supplied text.